There are actually a lot of labs out there that research this and it is a wide field. I would recommend reading current literature to see what aspects of relationship research you like the most. For instance, do you want to look at divorce prevention, relationship transitions (e.g. getting married, having kids), couples and stress, romantic relationships of a specific culture or group, etc. There is a wide variety of research going on.
Off the top of my head though, there is University of Denver, Georgia, Texas A & M, Hawaii, Rochester and Maimi. But those aren't even quarter of what's out there.