I don’t know any shooter split-screen game except for CoD, which apparently isn’t an option. But I can try to give other alternatives: Stikbold is an arcadey dodgeball game, Moving out is an Overcooked style game where you move furniture from houses, Untitled Goose Game is a stealth game (I don’t really know what genre it is) where you play as geese trying to mess with people and clear objectives and Unravel 2 is a platformer adventure game. The first two can also be played with more than two players.
I attempted to give many different genres here, so I hope that at least one will pique your interest.