If anyone is interested in increasing Push-ups for the two minute max, this is a good article from military.com. I've also seen people use resistance bands held in their hands wrapped around their backs to increase resistance for a cheap at-home increase to resistance for your push-up exercises. Don't forget proper form!
"Below is the program that has helped people go from 50 pushups to 80 pushups in two weeks.
On Odd Days
Do 200 pushups in as few sets as possible in addition to your regularly scheduled workout of cardio exercises. You can still do upper body workouts on these days if you are already on a program. This is a supplemental 200 pushups using maximum repetition sets (4 x 50, 8 x 25 ... it's your choice how you get to 200).
On Even Days
Do 200 pushups throughout the day. This can be little sets of ten done every half hour or fifty pushups done four times throughout the day.
Rule
If your maximum is under 50 pushups, do 200 a day. If your maximum is above 75, do 300 pushups a day.
Repeat the ODD/EVEN routine for a total of 10 days. Then take three days off and do NO upper body pushing exercises that work the chest, triceps, and shoulders. Then on day 14, give yourself the pushup test (one or two minutes depending on your PFT). I would not recommend this workout more than once every six months, since it rather challenging on the same muscle groups repeatedly.
There are three main types of pushups you can do to break up the monotony: "regular" pushups, "wide" pushups, and triceps pushups."