Originally Posted by
dtrain
Should be okay, but you'll just have to try them. I had some cheaper 23's that worked fine on traditional rims, but just wouldn't stay on my 23mm HED Belgium C2 rims. Seemed like that was too much stretch and the bead wouldn't hold. On my other set, Mich. PR3 23's seem just fine (on 24mm Pacenti SL23 rims)...but that's a nicer tire and runs a little wide.
I'm surprised to hear that about a 23c tire not fitting the C2s. The internal width, or BSW, of that rim is just 17.5mm, not particularly wide, and is well within spec range of 23c fitment.
Your SL23s, however, hit 20.3mm BSW, which is pretty wide, and perhaps a greater width than you'd expect just comparing the simple, external width numbers between it and the C2, which only varies by 1mm. Still, 23c tires should mount fine.
Anyway, besides emphasizing that external width is not the important number to tire fit (but can be important for brake setup), I'm wondering if bead shape might be the explanation for the problem you had, though that's typically not an issue for clinchers; pehaps an out of spec tire?