I'm happy if it's mostly a single player game, that's how it should be. I don't think coop would bring anything interesting, unless it is like Portal 2 and brings exclusive levels. Otherwise, if it's coop in the same set of levels as singleplayer, that would suck. Say one of the players finds the solution to a puzzle or deals the fatal blow to a boss, then the other player missed the fun part and will have to replay it on his own anyway to do it himself. So I'm fine without coop.
But it shouldn't preclude a multiplayer mode, say like the one in Conker's Bad Fur Day. This one was pretty fun, a bunch of minigames set in some of the main locations with goals that remind of the single player part of the game. I don't know if Project Ukulele will have as many different gameplays as Conker since Conker made heavy use of the context sensitive stuff, so it may not be possible to have a really Conker like multiplayer mode. But something in the same vein should be enough, simply take the parts of the singleplayer game that could be fun to play competitively against another player, I'm pretty sure there'll be a few like that, such as minigames, races, and so on, and make them multiplayer.
If there's some multiplayer at all, I'd love it to be online, that's a given.