There have been several good guesses today. It’s actually hard to declare a winner, since it somewhat depends on how you parse history. Basically, the two main groups that were considered for merger were the Congregationalists and the Christians. But it’s all part of how you define things.
For example, SophiaSeeker guesses that the United Church of Christ was one of the groups that the Unitarians and Universalists considered merging with. That’s sort of right, but only if we think of the UCC as the main inheritors of the Congregationalist legacy. But by the time the UCC was created in 1957, not only had it combined with German denominations that the U/Us had never flirted with, but the talk of possible merger was past. This seems to be what StevenR had in mind in his comment. Both the Unitarians and the Universalists considered merger with the pre-UCC Congregationalists at times, but the Universalists were significantly closer to an actual plan to do so.
Meanwhile, Philocrites correctly guessed the other, actually much earlier group that the Unitarians especially considered merger with. Even his answer technically needs some unpacking: in the early 19th century a broad movement called the Christians appeared that included a number of strands in it. The ones that the Unitarians worked with tended not to be the actual ones that directly gave rise to the Disciples of Christ, but again, this was a multi-faceted and protean movement, so it isn’t a wrong answer.
For post-UUA merger, there are two groups that have popped up repeatedly in UU circles (and sometimes on the other side of the fence as well) as potential future merger partners. Both happen to appear in StevenR’s speculations about groups that might merge with the UUA. One, predictably, is the UCC. The UCC and the UUA share common roots, although the Congregationalist UCC forbearers were actually bitter enemies of both the Unitarians and Universalists for quite some time, even actively persecuting them (especially the Universalists) in their New England stronghold. Of course, the idea of UCC folks persecuting anyone is so odd that it just shows how long ago all this was. A merger is not outside the bounds of imagination, though it might’ve worked better if the UUs had become the Liberal Christian Church as planned at one point, rather than the Unitarian Universalist Association.
The other possible merger partner is, believe it or not, actually the one that has been more strongly considered: Ethical Culture. Dana Greeley even speculated that such a merger was desirable and looked forward to the day that it might happen. But will either come about? Probably not in the short term, at least.