Ah, Unhappiness - the rightful bain of the Domination Victory. Especially if one makes an early domination rush, Unhappiness can be a game-long pain. You really have to plan for unhappiness if you're taking the Domination route.
As other players have suggested, it sounds like you're keeping a lot of cities you shouldn't. The small, crummy spam cities some AIs tend to build are of diminishing value to you, and should be immediately razed unless they have a resource you *really* need. While large cities give you a big unhappiness hit for the extra population you just added, at least you get the benefit of that population. Small cities give you the global unhappiness for the extra city plus a couple extra dings of unhappiness for their small population, all of which won't be made up by local happiness measures like buildings. Seriously, burn down those cities. They're unhelpful.
Capitals with a strong production ability should be annexed ASAP to build in the Courthouse and join in pumping out units.
I'll echo Fluffball here, the Liberty and Order policies are your friends if you're dominating a large map. Also, investing in a happiness-forming religion will serve you well with Global Happiness. Finally, if there's a wonder-spammer on your map, bee-lining for them usually means a capital ful of happiness-pumping wonders (if you can't build them yourself).