There is almost no downside to expanding as population is quickly capped in the early game. I think the problem can be mitigated by making unrest scale with expansion.
Once a city is contiguous to your capital it only produces 22% unrest which is easily covered by the belltower + cleric, or at most one more 10% building. There is no need to have any more unrest reduction unless you want to raise the tax rate (which is not beneficial until much later in the game).
The game needs an unrest penalty to check against rapid expansion, which is the only effective strategy (aside from overpowered custom soverigns). Each new city should add x% unrest to existing cities. It could be static 5% per new city or incremental (1%,2%,3%,4% etc), and it should be based on the map size / number of opponents.
This will create a downside to reckless expanding in the early game and a counter to the snowball effect in the late game, both of which are lacking in the current game. This will also allow the garrisoned unit reduces unrest effect suggested in another thread to have a purpose in countering the expansion unrest.