If your wrists are a problem before you arms give out you need to get a set of weights. Put them under you and wrap you hands around them. It keeps your wrists straight and allows you to do the push up after your wrists are tired.
I was able to many more this way after my wrists go sore.
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The other thing to do (along with a push up progressions already suggested) is to do the yoga poses and try to hold them for increasingly long intervals. I imagine you're probably working on downward facing dog, high plank, dolphin, and similar poses. Just hanging out in these poses will help your body get used to doing them and you'll eventually be able to hold them longer.
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