Considering the amount of space that space occupies, and the size of the cometary nucleus, as well as the nearly nil gravitational effect of one upon the other -- particularly at the speeds implied -- I would say that the event of one comet colliding with another would be extremely rare -- and for it to occur in a place that would create planetary rings, rarer still.

Jupiter has it's own set of comets, tiny orbiters that never come close enough to the Sun to flare into the comets we've come to know, and it is likely that Saturn has a set as well -- but I don't think this is nearly enough.

Also, how often does this occur? Uranus has a ring. Jupiter has a ring. It is theorized that Earth had a ring at one time. I think this is all heavy-impactor related.

Dan