I bought a Cooper off a member here and it shoots really well. Very pretty to look at too. So if you are looking for an American made sporter, it would be hard to do better. That said, mine is a sporter and my dedicated bench rifles will out-shoot the Cooper for groups, not, I think, because of any superiority of the barrel, but because I find a sporter a difficult rifle to return precisely to battery -- even on a rest -- shot after shot. That's where a dedicated BR stock really helps. All those straight lines at the forearm and buttstock make return to battery a cinch. Or put it another way: I think a better shooter could do better with my Cooper than I can, if that makes any sense. Take the following as just one man's opinion -- worth about what you are paying for it.
So for a current-production, American made bolt rifle in a sporter stock what else is out there? Quite a lot, actually. It is a great time to be interested in this stuff, but no one is making a direct competitor the Cooper, really. Closest in quality would be an Anschutz 1710 or 1712, but these are German. Marlin(!), Ruger and Savage make plenty of .22 LR models, but I have never shot one one that could compete with my Cooper on accuracy and looks. Vudoo rifles can be really accurate and they are American made -- they have a different design philosophy than the Coopers, but will make anything you want, as long as you like that big AICS magazine or want to shoot single shot. For a Vudoo sporter, look at their Sinister, Raven, or Crow models. And Vudoo seems to have blazed something of a trail as there are at least three companies trying to play in the same sandbox: Bergara (not US-made), Deuce Ultimatum (still in development?) and RimX. I haven't handled any of these but the Bergara and while it is a nice rifle, the Vudoo is better in about nine ways. These aren't really sporters either, although perhaps they could be configured that way. Henry's are nice, but not in the same league. Christiansen Arms has some models you might want to look at, although I have never handled, much less shot one.
If "American made" is off the table, I'd look at an Anschutz 54-action sporter. There are a lot more of these out there used than used Coopers and mine is just as accurate for 1/2 the price (used Annie vs. new Cooper). I'd also look at a Lithgow 101 or a Tikka TX-1.
Finally, there is the full custom option, and that's its own rabbit hole. But if you start with the premise that the accuracy of a .22 LR rifle is really mostly about the barrel, then you start with the barrel (Lilja, Shien, Kreiger, Bartlein - what-have-you) and move from there. A competent smith can chamber it for you and thread it to any action you choose.