This is where sizing is tough...and I like to post actual measurements when available. 2" = 58mm wide, if it's absolutely true to size, but we know that most tires are not true to nominal size. And, frustratingly, even though Schwalbe call it a 29x2, the ERTRO measurement is 50x622 (50mm diameter casing, on 622mm rim). That's very much not a 2" tire, but that's become the norm.

On your specific bike, what is the clearance between the chain stays near where the shoulder (side lugs) of the tread, would be? If it's about 50mm, and you think an actual 51mm tire would be too wide, you could look at any of a number of 47mm tires (they'll be marked 700x47 or 47-622). I know Schwalbe and Continental make a few in this size, plus others as well. Schwalbes are generally pretty true to the ERTRO size (a 50-622 is going to be close to 50mm wide, and a 47-622 is going to be close to 47mm wide), but Continental is often a fair bit smaller even than the ERTRO size. If your actual clearance is about 50mm, then a 45-47mm tire might be good (more selection in 45mm wide probably).