They need three things to become more popular:
Awesome rivals (preferably more than one)
More mic time
At least one EPIC match (preferably a "first-ever" match of some kind)
Matches against The Brian Kendrik and Matt/Regal just don't cut it. They need to feud with an already established tag team. The first team that might come to mind is the Miz and Morrison, but putting asside the fact that they've separated, they don't have the same appeal that the Dudley's or E&C did back in the Hardy's days. I think what they need is to get into a feud with another face tag team. Being that I don't typically watch SD or ECW, I can't think of any off the top of my head, but if they could have sort of a friendly feud with another face team, that could help boost them and the other team a little.
If they got more mic time, they would get more of a chance to get more over with the fans. Again, I only watch Raw, so maybe they get more time on SD and ECW-therefore making my point moot-but the idea is to give Carlito the mic and have him let the fans know how "cool" they are.
The match where I became a Hardy fan for life was the WrestleMania 2000 match. Before that, I knew of the Hardy's, but didn't really care about them. Once I saw that match, my interest jumped up about 1200% and still hasn't declined much. If the Colon's can get a ground-breaking match like that (and if the wwe will TELEVISE IT this time) then that could deffinetly catapult them into the epicness that they are capable of.
Unfortunatly, all of this is pointless banter, seeing as how Vince doesn't give a damn about the tag team division, and would probably like to get rid of the tag titles all together.