I've a number of ideas for buildings, but I need a few days to sit down and compite/rationalize them.
Here's an easy, quick one, though...
Tourney - same effect as Theatre... possible that it gives +experience for knight type units (I think this is only possible for Warlords). Arab/Egypt/Turkic equivalent would possibly be a horse/camel racing competitive event.
also, national wonder... Grand or Royal Tourney... equivalent effects to Globe Theatre national wonder.
Both these would require that you choose some tech on which to allow the influence (culture) slider to be adjusted to change the happiness output. Since it is influence rather than culture used in this mod, I suggest some sort of government, noble or state power related tech.
I have numerous other suggestions, but I need to develope the ideas further, then I'll bring them forward.