I know there are trout in Rock Creek, but I've never fished it.
As far as the river goes, catfish reign supreme. At times, the catfishing can be really easy, great for kids. While targeting the catfish, you may hook into a big fat carp or some roundtail chubs. The roundtails must be released as they are a protected species.
It is also theoretically possible to catch a smallmouth bass, walleye, or pikeminnow, but you are not likely to have much luck targeting them. As per Utah fishing regulations, smallmouth bass, northern pike, walleye, and a few other species may not be returned alive to the Green River if caught. Of course, pikeminnow are a federal endangered species and must be released immediately back into the river if you are lucky enough to catch one.