I know from experience that every time we post about a local multiplayer game, someone somewhere is grumpy because their couch doesn't connect to the internet and so they have no one to play it with. ChargeShot [official site] might still appeal: it's a single-screen local multiplayer game about shooting big, bouncing bullets, but it's also got a solid singleplayer mode against bots. Find trailers for both below - along with a few thoughts based on 30 minutes playing the game.
The closest comparison is probably Samurai Gunn, but instead of knives, you've a cannon with a long reload time between each shot and a shield that you can activate for half-a-second at a time. Your bullets rebound off walls once before exploding, but you can also use your shield to deflect them. When combined with the jetpack you use for getting around, the game becomes about timing and reflex. You'll drop in front of an enemy and have a split second to fire in order to kill them, whereas they have the same split second to deflect that bullet back in your face.
The singleplayer campaign has you moving from planet to planet, fighting different foes in one-on-one fights while a finite pool of lives ticks down. Each level has a centerpiece that becomes part of your strategy: a spewing geyser of steam, swinging lanterns that set you on fire when touched, a layer of lava that periodically rises towards the top of the screen. The enemy AI isn't always smart enough to deal with these obstacles, but they seemed considerably smarter than me as I set myself on fire with the lanterns over and over. They're good enough, anyway, to maintain that central challenge of timing.
Chargeshot is a pretty simple game, and I'd say based on my brief experience that it lacks the precision or polish of yer Samurai Gunns, Nidhoggs, and TowerFalls, but I had fun. It's currently £5.59 on Steam.
Here's the singleplayer trailer:
And here's the multiplayer trailer: