I tried this method a decade ago during my sport studies. Worked really well for me and a couple of my peers (the ones actually going through with it).
I don’t know if it works as good on other body weight exercises. Probably, but unlike chins, push-ups can be done anywhere at any time so it’s easier to follow the program.
First, test your current max. Do as many push-ups as you can, note that number and calculate half of it. If you hit an uneven number of reps, round up. If you hit 14 reps, your submax will be 7 reps. If you hit 15 reps, your submax will be 8 reps.
Now, perform one set of your submax reps every third hour, every day, for 14 days straight. I usually end up with 5 times a day. On day 15, test your max again, calculate a new submax and do another 14-day routine.
That’s it! Simple but effective.