“Please” is a nice way to ask for something. By at least the 1880s, children were begging their parents with “pretty please.” “Pretty please, with sugar on it” was cited in print in January 1912. By 1914, someone asked, “Pretty please with kisses on it?”
 
“Pretty please, with sugar on top, and a cherry” soon followed. The expression is dated—“Pretty please, with aspartame on top” never worked—but it is still used today.
   
 
(Oxford English Dictionary)
pretty please adv. [compare German bitte schön] colloq. used in emphatically polite or imploring request; cf. PLEASE adv.
[1891 R. T. COOKE Huckleberries 169 Say ‘please’ now—real pretty.]
1913 Indianapolis Star 29 Jan. 16/4 She begged him with ‘please’ and ‘*pretty please’ to see her.
1925 S. V. BENÉT Tiger Joy 27 Never had a mammy to teach me pretty-please.
1959 A. SINCLAIR Breaking of Bumbo v. 74 She was saying, Please. Pretty please.
1964 Time 28 Feb. 28/3 Can I, pretty please?
1973 C. MASON Hostage vii. 106 Pretty please, with sugar on it.
1994 Q. TARANTINO & R. AVARY Pulp Fiction iv. 156, I need you guys to act fast if you want to get out of this. So pretty please, with sugar on top, clean the fuckin’ car.
 
2 December 1888, Daily Inter Ocean (Chicago, IL), “The Beginnings of Beauty” by Shirley Dare, pg. 21, col. 2:
It does not seem necessary to say “please” or “thank you,” for hourly service, counted in the bond, either to servants or children, but they can be told to do things in a pleasant way, that is as far from domineering as it is from the “pretty please” fashion.
     
Google Books
January 1912, Equity Series (Philadelphia, PA), “An Era in Charter Making,” pg. 4, col. 1:
There is an earnest association of cities of the third class which is striving for the privilege of freedom in charter making, and if the oppressed people say “Please” to Senator Penrose, with sufficient humility—“Pretty please, with sugar on it;” and swear to support the machine ever after—they may be allowed that privilege some time in the future.
 
9 February 1912, St. Petersburg (FL) Daily Times, “An Era of Charter Making” by Equity Series, pg. 2, col. 3:
There is an earnest association of cities of the third class which is striving for the privilege of freedom in charter making, and if the oppressed people say “Please” to Senator Penrose, with sufficient humility—“Pretty please, with sugar on it;” and swear to support the machine ever after—they may be allowed that privilege some time in the future.
 
Google Books
My Lady’s Garter
By Jacques Futrelle
New York, NY: Hodder and Stoughton
1914
Pg. 24:
“Pretty please with kisses on it?”
“No!!!”
 
Google News Archive
13 January 1917, The Day (New London, CT), “Timely Views By The Commentator,” pg. 6, col. 3:
All you have to do is to say “Please—pretty please, with sugar on it” and I’ll come through with almost any sort of stunt, if I can.
     
28 August 1927, Charleston (WV) Gazette, “Sally’s Shoulders” by Beatrice Burton, pg. 11, col. 1:
“Please—pretty please with sugar on it,” she pleaded, childishly. 
 
8 June 1929, Lethbridge (Alberta, Canada) Herald, “The Golden Girl” by Barbara Webb, pg. 13, col. 5:
“Oh, come on, So-so. Please, So-so. Pretty please, pretty please with sugar on it, lots of sugar—.”
 
Google BOoks
Alfred, Ahoy!
By Foster Humfreville and Gurney Williams
Published by R. M. McBride & Co.
1944
Pg. 28:
“No! We’ve said ‘please’ and ‘pretty please,’ but we are not going to say ‘pretty please with sugar on it.’”
   
Google Books
They Ask for Bread:
A Novel
By Rebecca Rogers
Published by Rockport Press, Inc.
On verso of t.p.: Printed by Grenich Printing Corp., New York
1946
Pg. 57: 
“Maybe if you were to sit in your Aunt Mathilda’s lap and ask her pretty please with sugar on it, she’d say yes.”
 
Time magazine
Please, with Sugar on It
Monday, Feb. 03, 1947
After months of being pestered to take controls off business, Washington was surprised last week by a new request: sugar growers and refiners pleaded unanimously for continuation of Government controls and sugar rationing.
 
Google Books
Clarence Day’s Life with Mother
By Howard Lindsay and Russel Crouse
New York, NY: Dramatists Play Service, Inc.
1950 (Originally staged October 20, 1948)
Pg. 55:
BESSIE. Clare, if you don’t do it right away I’m going to make you say “Pretty please with sugar on it!”
 
Google News Archive
24 December 1954, Malakoff (TX)  News, “Letters To Santa Claus,” pg. ?, col. 2:
I want a sender and receiver set. I’m 7 years old. And some cowboy’s and Indians. Pretty please with sugar in it.
 
Google Books
The Adventures of Harlequin
Comedy by William Glennon
Chicago, IL: Coach House Press
1963
Pg. 16:
TINA. Please, Mama.
MAMA. No.
RENATO. Pretty please?
MAMA. No.
HARLEQUIN. Pretty please, with sugar on it?
MAMA. No.
LUIGI. Pretty please, with sugar and cream and strawberries on it?
MAMA. Show us.
 
OCLC WorldCat record
“Pleeeeease, with sugar on top?!?” : children’s and parents’ perceptions of television use and food advertising
by Ameena Batada
Type:  Thesis/dissertation : Manuscript Archival Material; English
Publisher: 2005.
Dissertation: Thesis (Dr. P.H.)—Johns Hopkins University, 2005.