Really?
Sam gets Rosie. There is a fine Hobbit romance.
Aaragorn gets Arwen. Tolkien isn't above a little cross-racial relationship or two.
For purely human romance, Éowyn gets over her love for Aragorn and gets Faramir.
Legolas loses his heart, OK that is to the sea and not a person, but still he does.
Heck, even Gollum gets his heart's desire, the Ring, and keeps it to the end of his days. (OK, that isn't as long as Gollum might have wished...)
Now the romance is not central to the book. Doing romances isn't exactly Tolkein's strong point. Wistful longing and deep devotion are more his style. There is a .. gap .. between feeling and lifelong marriage that he doesn't fill in. But still there were romances there.
Cheers,
Ben