Is there any way to make your wrists stronger (for push-ups)

http://www.amazon.com/Everlast-EX2431BK-Wrist-Strengthener/dp/B00091RXT6

http://www.amazon.com/Dynaflex-Powerball-Glowing-Amber-Lights/dp/B000WO858S

are you certain that this pain is due to weak wrist muscles?
Can you describe the pain in a bit more detail? (location, type of pain (throbbing, sharp, or otherwise), motions which cause it)
@syz those links don’t work.

Get a wrist strengthener, like the ones Syz posted (if the links don’t work, just search for the names in the URL.)

Personally, I’d start doing fist pushups instead of open palm ones. It’s less strain on your wrist as a fist is a more natural position.

I know of something that can make your wrists stronger ;)

LOL

I have been using the Perfect Pushup stands and they cause me no wrist pain. I do 1800 a week. Try them out to see if it helps.

Sounds like you may have tendinitus of the hand. You say wrist but then you say the pain is in the palm of your hand. If it is tendinitus it comes from repetative motion or strain. You need to pack ice on it and let it rest. For more information read this link.
http://www.arthritis-pain-cure.com/tendinitis_hand.html

@LocoLuke The pain is more sharp while I do push-ups, then throbbing once I am done.