This one is a bit of a tough call. There are three viable players who will be competing for these two spots come Spring Training - they are Adam Moore, Rob Johnson, and Josh Bard.
Moore is the Seattle Mariners' catcher of the future and one of the best prospects in the Mariners' system. Based on his 2009 performance down in Triple-A, he may finally be ready to break into the big leagues—whether or not the team gives him that opportunity will almost certainly depend on how well he performs in Spring Training.
Rob Johnson is clearly a favorite of this organization, despite the fact that his offense is awful and he apparently lacks the ability to consistently catch fastballs. He had several major surgeries this off-season to rectify various health issues. How his recovery is going will certainly be a factor when it comes to his eventual role.
Josh Bard would certainly be an okay choice, but I don't see him making the team out of camp. One thing he has going for him is the fact that he's a switch hitter, but that's about it. He isn't a real good hitter from either side of the plate, and his ability to throw runners out has been in question throughout his career.
I have no doubt that, whatever route the team decides to take, the catcher situation will be much closer to a 50/50 playing time split than to a starter/backup type of thing.