Unfortunately, I couldn't find any early citations. The earliest citations appear to come from San Francisco, not New York City. But if you're got a legitimate citation, I'll post it here.
12 September 1943, Washington Post, pg. R2:
Naturally the idea would have been barren of results without the full cooperation of the restaurants, so samples of Pet Pakit bags and Pet Pakit bag dispensers were made up and submitted to the San Francisco Restaurant Association, together with an explanation of what they would accomplish.
26 June 1947, Washingron Post, "Bones for Bowser," pg. B2:
Now all that is changed. Dinners from which bones may be salvaged are accompanied by a wax-lined paper bag inscribed as follows:
Are you happy over dinner?
Don't have all the fun alone.
Remember the pup who's waiting
And take him a luscious bone.
July 1947, Marchant Restaurateur Magazine, pg. 20, col. 1:
They're Kind to Animals in Tacoma!
Tacoma Cafe Starts Unique Service For Patrons' Dogs
THE New Yorker Cafe in Tacoma, Washington, has recently instituted a personalized service for its customers with a novel and original "Snack-Sac," a glacin lined, grease proof bag in which patrons may take home bones and other food scraps for their pets. Patrons also find the "Snack-Sac" a handy container in which to take home excess portions of meat and pastry for themselves.
This attractive "Snack-Sac" done in two colors shows an appealing and hungry dog saying "Dog-Gonit...I hope they don't forget my New Yorker Cafe 'Snack-Sac'."
September 1952, American Restaurant Magazine, pg. 164:
IT'S A PLEASURE
to hand this beautiful
to your patrons
TO TAKE HOME BONES FOR THEIR DOG
Sturdy, holds large steak bones. Printed in three colors. You must see
this, it's the kind of advertising they will talk about. It's class.
YOUR NAME AND ADDRESS ON EVERY PAK
DOGGIE PAK CO. 600 South Michigan Blvd., Chicago 5, Ill.
April 1954, American Restaurant Magazine, pg. 84"
Bones for the Dog
"Finale. If you have a pooch at home, the Leonards invite you to take home a box of sirloin bones to pamper the palate of your favorite pup."
February 1955, Diner, Drive-In and Restaurant, pg. 50, col. 2:
A new and attractive carton for leftover steak bones and other meat for pets has been introduced by the Doggie-Pak Company. The new carton resembles a miniature dog house complete with a roof and a door out of which a pair of canine eyes gaze appealingly.
The new 8 by 4 1/2 by 3 inch carton, designed to hold plenty of scraps, is available in three colors - turquoise, red and black - with a blank panel located on one side for the name and address of the establishment.
December 1959, Fast Food, pg. 24, col. 1:
>i>Lucky Dogs - Archie's Lobster House near Roanoke, Va., hasn't gone to the dogs - but dogs are coming to it.
Near the restaurant's parking area is a "pet restaurant," carefully penned in with a place for tying Fido. While customers are inside the restaurant having their meal, the management provides special plate service for the chow hounds in the pet department.
It's Archie's addition to the more common service of providing a bag to customers who want to take scraps home to their pets. And Archie's has that, too - a neatly lined paper bag with the slogan: "Make him happy - take scraps home for your pet."
September 1960, Fast Food, pg. 78, col. 1:
Guests can take home scraps for their pets without mess or bother; grease proof; in stock