I think UB-2 had a small brass ring.
I don't know if you are building a new one or fixing up an old, but...
FYI- There is no universal banjo uke part. If you ordered something online without thinking about diameter and height of the tone ring, it may not fit. banjo uke rims come in a myriad of sizes from 6-10 inches. Also, adding a tone ring to an existing instrument (if it fits on the rim) may throw the geometry off by pushing the head up into the path of where the strings are supposed to go down towards the neck.
Also, most rims are machined to fit the tone ring on the top so that the ring doesn't float around. You may be able to get it to stay on a flat segment of rim, or you may not.
Are you stretching a skin head or using a pre made one? Some heads don't have a deep enough crown to fit over the brass ring and reach all the way down under the tension hoop. fyi.