Dr. Brown’s Celery Tonic was (according to the company) first produced in 1868 in Brooklyn. The Food and Drug Administration objected to its being called a “tonic,” and in the 1900s the name was changed to Dr. Brown’s Cel-Ray (soda). The taste is somewhat similar to ginger ale. Dr. Brown’s briefly produced a diet Cel-Ray, but it was discontinued. Other “celery tonics”/“celery sodas” were produced in the 1890s, but only Dr. Brown’s celery product remains.
 
Dr. Brown’s sodas are kosher and can be found in many delis. Dr. Brown’s Cel-Ray was so popular with New York’s Jewish community that the product was called Jewish champagne in the 1930s.
 
 
Wikipedia: Cel-Ray
Dr Brown’s Cel-Ray soda is a soft drink with a celery flavor. It is fairly easy to find in New York City. Outside the New York City region, it is rather obscure but can sometimes be found at Jewish delicatessens and restaurants. In addition, it can be found at certain grocers that specialize in American food in Israel, and other specialty grocers.

The flavor is reminiscent of ginger ale, but with a more pronounced celery flavor that is more pungent or peppery, derived from celery seed extract.

The diet version of Cel-Ray soda has been discontinued.
     
Wikipedia: Dr. Brown’s
Dr. Brown’s is a brand of soft drink bottled by Canada Dry. It is a popular brand in the New York City region, but it can also be found in Jewish delicatessens and upscale supermarkets around the United States.
 
Dr. Brown’s varieties include:

. cream soda (regular and diet),
. black cherry soda (regular and diet),
. orange soda,
. ginger ale,
. root beer, and
. Cel-Ray (celery-flavored soda).
 
Dr. Brown’s soda is typically sold in 12-ounce cans and in one-liter and plastic bottles as well as two-liters in Black Cherry, Cream, and Root Beer flavors. (Less common are Dr. Brown’s 12-ounce glass bottles.)
   
22 January 1889, Kansas City (MO) Star, pg. 3, col. 8:
His physicians have put him on a very strong celery tonic.
         
22 August 1899, Woodland (CA) Daily Democrat, pg. 1, col. 2:
A new corporation has just been formed of $50,000, fully subscribed, to manufacture in San Francisco an ENglish preparation, Celery Soda, which will be introduced in the United States as a harmless, yet effective cure for headache, nervousness, biliousness and sleeplessness.
 
11 June 1916, New York (NY) Times, pg. XX1 ad:
Dr. Brown’s Celery Tonic
Delicious, thirst quenching, healthful beverage; per dozen bottles (rebate on empties)...$1.00
 
22 February 1984, New York (NY) Times, “Dr. Brown in Market Expansion; National Push for Deli Soda,” pg. D4:
After more than a half-centuiry as a best seller in Jewish delicatessens in New yrok, Dr. Brown’s soda is setting out to make its name known in the world at large.
 
In the process, the 115-year-old brand hopes to broaden the market for its most popular flavors—cream, balck cherry and Cel-Ray, or celery-flavored, sodas—without losing its ethnic following.
(...)
The brand has been around since 1869 when, as legend has it, a Dr. Brown from the Williamsburg section of Brooklyn produced a celery soda and persuaded a friend at the Scholz Bottling Company to market it as a celery tonic, according to Mr. Berberich.
(...)
“Dr. Brown’s is a cult drink to those of us who grew up in New York,” he said. 
 
9 June 1984 New York (NY) Times, “Q. What is a ‘Dixie’? A. A Kind of Walker” by Howard Topoff, pg. 23:
4. Dr. Brown is best known for
(a) Founding Bushwick Hospital.
(b) Being the first president of Brooklyn College.
(c) Making the world’s best cream soda.
(...)
ANSWERS
4. (c) His Celery Tonic and Black Cherry Soda, also first rate, are especially good with hot pastrami.
       
Google Books
Jewish Farmers of the Catskills:
A Century of Survival
By Abraham D. Lavender, Clarence B. Steinberg
Published by University Press of Florida
1995
Pg. 178:
Another New York City emblem was ubiquitous at these buffets: the ornately labeled Dr. Brown’s bottles containing cream soda, ginger ale, or celery tonic
       
New York (NY) Times
Dr. Brown’s Cel-Ray Tonic
By BERNARD COOPER
Published: March 10, 1996
WHEN MY PARENTS took me to eat at Canter’s delicatessen, I invariably ordered a Dr. Brown’s Cel-Ray Tonic; it was the only soft drink my mother sanctioned, believing that its trace of vegetable matter (extract of celery seed was a mere footnote in the long list of ingredients) would fortify a growing boy. Medicinal or not, I loved the exhilarating sting of carbonation, the delicate hint of vanilla and the icy, mouth-dousing sweetness.
 
The glass bottles gave no clue as to the identity of Dr. Brown, and yet I pictured him as a kindly, white-coated man not unlike my dentist. In a pristine laboratory filled with bubbling test tubes and beakers, Dr. Brown concocted the amber elixir that washed away the saltiness of corned beef, cut the peppery after-burn of pastrami or kept me from choking on a throatful of brisket. When I took a swig of Cel-Ray Tonic, I never thought about anything as mundane as a stalk of celery—instead, I saw cells dividing and recombining, ray guns shooting beams of light. Every gulp was a toast to the future, each bottle a triumph of science.
 
(Trademark)
Word Mark DR. BROWN’S CEL-RAY
Goods and Services IC 032. US 045 046 048. G & S: non-alcoholic beverages, namely, carbonated beverages. FIRST USE: 19300000. FIRST USE IN COMMERCE: 19300000
Standard Characters Claimed
Mark Drawing Code (4) STANDARD CHARACTER MARK
Serial Number 78628091
Filing Date May 11, 2005
Current Filing Basis 1A
Original Filing Basis 1A
Published for Opposition January 31, 2006
Registration Number 3085397
Registration Date April 25, 2006
Owner (REGISTRANT) Canada Dry Bottling Company of New York CDNY Corp., a Pennsylvania corporation LIMITED PARTNERSHIP NEW YORK 112-02 Fifteenth Avenue College Point NEW YORK 11356
Attorney of Record Peter T. Wakiyama, Esquire
Prior Registrations 0589144;1365860;1366958;AND OTHERS
Type of Mark TRADEMARK
Register PRINCIPAL
Live/Dead Indicator LIVE
 
(Trademark)
Word Mark “THE ONLY GENUINE SINCE 1868” DR.BROWN’S CEL-RAY A CARBONATED CELERY BEVERAGE DB
Goods and Services (EXPIRED) IC 032. US 045. G & S: CELERY BEVERAGE SOLD AS A MALTLESS SOFT DRINK. FIRST USE: 19370603. FIRST USE IN COMMERCE: 19370603
Mark Drawing Code (3) DESIGN PLUS WORDS, LETTERS, AND/OR NUMBERS
Design Search Code 01.15.25 - Coal; Dust; Light rays; Liquids, spilling; Pouring liquids; Sand; Spilling liquids
26.01.17 - Circles, two concentric; Concentric circles, two; Two concentric circles
26.11.25 - Rectangles with one or more curved sides
26.17.25 - Other lines, bands or bars
Serial Number 71541627
Filing Date November 19, 1947
Current Filing Basis 1A
Original Filing Basis 1A
Registration Number 0511842
Registration Date July 5, 1949
Owner (REGISTRANT) AMERICAN BEVERAGE CORPORATION CORPORATION DELAWARE 118 NORTH 11TH STREET BROOKLYN NEW YORK
(LAST LISTED OWNER) PEPSI-COLA BOTTLING COMPANY OF NEW YORK, INC. CORPORATION BY MERGER WITH PENNSYLVANIA 112-02 15TH AVENUE COLLEGE POINT NEW YORK 11356
Assignment Recorded ASSIGNMENT RECORDED
Prior Registrations 0063371;0064229;0082628;0183212;0228759;0293635
Disclaimer NO CLAIM BEING MADE TO THE EXCLUSIVE USE OF THE WORDS “A CARBONATED CELERY BEVERAGE” AND “THE ONLY GENUINE SINCE 1868” APART FROM THE MARK AS SHOWN IN THE DRAWING.
Type of Mark TRADEMARK
Register PRINCIPAL-2(F)
Affidavit Text SECT 15.
Renewal 2ND RENEWAL 19950131
Other Data SAID NAME “DR. BROWN’S” BEING FANCIFUL.
Live/Dead Indicator DEAD
   
(Trademark)
Word Mark DR. BROWN’S
Goods and Services IC 032. US 045. G & S: NONALCOHOLIC, NONCEREAL, MALTLESS BEVERAGES SOLD AS SOFT DRINKS-NAMELY, GINGER ALE, [ SARSAPARILLA, ] CELERY, LEMON SODA AND CREAM SODA. FIRST USE: 18860000. FIRST USE IN COMMERCE: 18860000
Mark Drawing Code (5) WORDS, LETTERS, AND/OR NUMBERS IN STYLIZED FORM
Serial Number 71189587
Filing Date December 12, 1923
Current Filing Basis 1A
Original Filing Basis 1A
Change In Registration CHANGE IN REGISTRATION HAS OCCURRED
Registration Number 0183212
Registration Date April 22, 1924
Owner (REGISTRANT) SCHONEBERGER & NOBLE, INC. CORPORATION NEW YORK 670-672 WATER STREET NEW YORK NEW YORK
(LAST LISTED OWNER) KIRSCH BEVERAGES, INC. CORPORATION ASSIGNEE OF NEW YORK 112-02 FIFTEENTH AVENUE COLLEGE POINT NEW YORK 11356
Assignment Recorded ASSIGNMENT RECORDED
Prior Registrations 0082628
Type of Mark TRADEMARK
Register PRINCIPAL
Renewal 3RD RENEWAL 19840422
Live/Dead Indicator LIVE