I've been going down this very road for years - though admittedly it is an off and on trek.
The standard primer for the .22 Jet cartridge is the Remington 6 1/2 small rifle primer.
DuPont, now marketed as IMR, publishes 13.5 grains of 4227 with the original 40 grain Jet bullet as giving a velocity of 2290 in a 10 inch barrel. Remington brass is used in this load, as is their 6 1/2 rifle primer.
DuPont and IMR both suggest a load reduction of 10 percent from the 13.5 provided, and working up to the 13.5 grain maximum based on pressure indications.
No information is provided regarding the type of barrel or firearm used in the load development. This could have been a pressure barrel or Contender pistol so be prudent in working with a Model 53 revolver.
John Traveler is correct. I requested load data from Remington and was sent the same information.
The difficulty with Jets is that they have a .222 bore and most varmint bullets are .224. Hornady does make a .222 diameter bullet for the Jet. Remington factory bullets for the Jet are no longer produced, which is a pity, as they were remarkable performers.
If you are so inclined, Remington can be contacted at 1-800-243-9700 (press 4) and you can request Remington produce a limited run of Jet bullets. I've done this and if enough of us make this request, Remington may get on board.
This may be more than you asked for but I think it answers your question.