Ah, I see Marduk already mentioned my Maya idea.
A fun one, but the problem being: if you're having a bad game, you could literally have this ability not proc even once.
It is a problem, and that's the point. The UA challenges the player. You gotta go in with the plan to milk it, and choose your techs and sopols wisely.
In thread after thread when folks present their ideas for UA's, it's disappointing so how they predominantly come up with boring "bonus food for such-and-such terrain, bonus science for such-and-such buildings, bonus hammers for such-and-such strategic resources, bonus happiness for such-and-such luxury--oh, and how about some more gold from trade routes?" stuff. Reliable, consistent, and no strategy required. Play the game just like before, just with some freebies thrown in. Walk the bases until you reach home plate.
Certainly there are UA's that just hand out freebies (e.g. Russia or France). However, there's plenty of precedence for this amongst existing civ's. If you're playing Germany, Ottomans, or Songhai, for instance, you gotta go barb-hunting while they're in bloom. What are Rome's UU's worth without iron, or Mongolia's without a good supply of horses? The Incas encourage you to go hunting for mountains while Polynesia incentivizes you to find unobstructed coastlines. And Spain's the most fun of all to play IMO, because it offers a high risk/reward ratio for exploration.
More specifically, it'll be virtually useless on harder difficulties.
Why? Because on higher difficulties, you can't compete to be first at anything? No matter what choices you make, you just don't have a chance? The thing about the Cycles of Sun and Moon UA is that it isn't luck-of-the-draw like all of those UA's that require you to pray for a favorable map. Research and sopols are largely map-agnostic, and you have multiple angles to pursue. You might pursue a tech or sopol just because you don't think anyone else will go for it right away. You might go all out pursuing the Oracle or Great Library. You might keep your empire compact to retain an edge on sopol costs and find yourself snowballing science. To not have the UA proc once during a game amounts to not coming up with a strategy.
Having said all that, the other uniques that go with that UA should, of course, compliment it and give you an edge towards being first. Along with the UI, I suggested a UI (step pyramid) and UB (e group) that would give an early slight edge in culture or science.
That isn't a very good design for Mayan. Too general.
I would give them a bonuses for wonder completions. 50% enhanced bonuses for World Wonder construction.
How are bonuses to wonder completion not too general? How are world wonders part of Maya's distinctive identity? OK, there's Chichen Itza. Whate else?
What's most remarkable about the Mayans wasn't the physical works they produced, but rather the way they took their folklore and religious beliefs and used them to fuel scientific research rather than put themselves at odds with it.