Between your price range and the type of game you are looking for, I really dont know...there arent tons of titles like that out there. Theres always the Modernwarfare specOps missons, and the original Amry of Two.
Hm, the only game that comes to my mind would be Realms of the Ancient War. There is a demo, I suggest that you try it out before you might decide to buy it. It's not really much of a RPG, more a simple and cheap Diablo wannabe.
Perhaps you should also mention too if you guys want to play together on one screen or if each of you has access to his own PS3 & TV.
Co-Op Role-Playing games (or with RPG elements) for under $20?
"Payday: The Heist"
"Trine" and "Trine 2"
And, as mentioned above: "Borderlands."
Just to name a few.
All have offline / online co-op.
I hope you find something you two will enjoy.
Awhile back Dungeon Hunter: Alliance was available for just a buck on the PlayStation Store. As a hack 'n slash-style dungeon crawler, you and others online can venture into dungeons and rid them of goblins and scores of other creatures types. More recently Borderlands 2 was on sale for $20 through PlayStation Plus. The first game also went free last year.
But if you decide to look for games on sale in other places, not just in the PlayStation Store, then getting yourself physical copies of titles might do you some good (in saving you some money). Though, such co-op games that come to mind on the store that are $20 or below consist of the following:
Ratchet and Clank: Full Frontal Assault
Payday: The Heist
Portal 2 is currently selling for a smidgen over $20 on Amazon, if you don't mind paying a few bucks for more a fantastic co-op game.