With a fair 'one person buys' setup
The other day I ran across a newly released shooter for iOS and Android called Dual. The whole gimmick is that it uses two devices to function, with a screen that spans between them. By forming a tenuous Voltron-esque link you can play two modes, versus and co-op.
Although it is a free download, thankfully, only one person needs to buy the premium version ($1.99) to play the latter mode.
The concept is simple but fun in short spurts, leading to some tense versus matches, but co-op is probably where its legs lie. The proper term for the mode is "Defense," tasking both players with stopping CPU ships from crashing into the middle and taking off a bit of your shared health bar. You'll have to work together in a big way as you swipe to flip directions, fending off both your side and your partner's, while dealing with elite enemies that can only be killed by certain players.
Although there's no bombs or other advanced features (a shot and charged shot is all you'll get), it's actually fun to learn the ins and outs of patterns and formations, and I was able to improve incrementally with my partner the more way played. Working together right next to reach other really brings back the magic of couch gaming.
There is one caveat though for the "one person buys" scheme though that should be mentioned. Said buyer will get the other two premium ships in their package in addition to the standard loadout -- the non-buyer will have to stick with just the one.