It would be cool if you could only build the appropriate wonder while you were in the appropriate government, and the bonuses interacted with the government bonuses, both currently and in the future. By pegging the bonus to the legacy government bonus, the wonder could go not entirely obsolete, and its permanent bonus would be based on how long you stayed in its government.
Like the Autocracy wonder could be Valley of the Kings. You can only build it in Autocracy, and when finished, it doubles your wonder-building bonus from the Autocracy government from 10% to 20%. After you switch out of Autocracy, it doubles your legacy bonus, say, from 3% to 6%.
The Oligarchy wonder could be something like the Daisen Kofun (the Kofuns in general being tombs from the era when the Emperor of Japan was still consolidating power, and there were lots of prominent people who got big Kofuns, not just the Emperor - this is a tricky one because governments don't usually call themselves oligarchies). In Oligarchy it doubles your experience bonus for military units, after Oligarchy it doubles the legacy bonus.
Then the Classical Republic wonder could be the Parthenon, and it doubles great people production under the Classical Republic, but then doubles the legacy bonus after it.
Other ideas (and it occurs to me you'd have to balance them all differently):
Monarchy - Versailles has to be built in your capital, but two tiles away from it, and gives you bonus influence points
Theocracy - Mahamaham Tank has to be built in a tile with access to fresh water within a tile of a road, and further reduces the cost of theocracy unit purchases (this wonder would probably have to be really expensive)
Merchant Republic - Dam Square has to be built on the coast and adjacent to a river and reduces the cost of gold purchases
And then the modern ones are probably the stuff people talked about above
Maybe you could also add that each government wonder provides an additional adjacency bonus to all districts it is adjacent to as long as you are in its government - in the primary yield of that district (like putting a campus right next to Versailles during a Monarchy gives it +1 science). Then the government wonder bonuses could synergize with the economic policies that double district adjacency bonuses.
One thing I like about this idea is it gives you some incentive to be in a different government than your competitors, which right now the game doesn't reward and just punishes.
EDIT -- Although now I'm wondering if Classical Republic is meant to represent Ancient Greek Democracy (maybe?) - or whether the Democracy was Oligarchic - that's confusing with the way the bonuses work.
Maybe instead all the ancient/classical government wonders are monuments to the dead - maybe the Classical Republic one could be called "The Gracchi" and refer to the statues of the Gracchus brothers that were put up all over Rome and venerated by the people after their murder?
