The 37 trigger is different than the other Kenyon triggers.
With the 37 you need to have a hole drilled into the bolt raceway about 1/4 inch ahead of the rear tang screw. Hopefully your 37 is so drilled. That hole is the access hole for the WOP adjustment. The screw in the trigger housing is for the sear catch.....and needs to be verrrrrrry carefully adjusted. The trigger MAY mount on the rifle without first drilling the access hole but it makes adjusting WOP a pain.
I have both types of Kenyon triggers for 37's; one with a flat blade (looks like it was made by Anschutz) and one is the early curved blade. Both triggers are exactly the same inside.
Karl sent an instruction sheet with each trigger. His cleaning instruction is to take the trigger apart (4 or 5 screws removes the side plate) but never ever remove the pins holding the guts to the other plate. Karl said to clean it with WD40. Me, I have done that but prefer lighter fluid. When you have taken the side plate off it is very easy to see just how ingenious Karls' triggers are. They are simplicity inside. What you cannot see is the different heat treatments Karl did to each little piece (the secret to his success in my opinion).
If you PM me I'll gladly e-mail you a copy of Karls' Instructions in PDF. Yes you got very lucky to find a Kenyon on your 37. I have only 2 37 Kenyon triggers and would love to have a few more. bob