My son puts a game in the PS2 and the door closes and then pops back open pushing the game out. Any suggestions on how to fix this problem?

Is it just one disc or all of them ?
Is this a legal PS2 game or a copy?
Is the disc dirty??

If you have the older ps2 then you should get the skinny one but from my experience the skinny ps2 sucks too for me so I'm getting a xbox 360. I know the older ps2 has that fan that gets dusty and defective.Also look at how you put the game in. don't push it in. use the button... that happened to my cousin.

I think it could be the console rejecting the disk

this could be either
-a totally unread-able disk
-a faulty 'door' =this is unlikely if it opens/closes normally
-the illegal/chipped ps2's don't have this problem because they are chipped so its not that.
-sometimes ps2's do that if they over-heat, they are sort of requesting a rest. Tell your son to leave it for a day and keep it in a cool place with lots a air so it can 'breathe' or ventilate.

if it still doesn't work id get it fixed or go on eBay and buy a new one.they are very cheap nowadays.