Slitherine

My last two achievements are for building the Great Lighthouse and the Coliseum. Other than an Egyptian and Roman game, what do I need to do?

if the historic faction doesn't build them then they become open to all. I've built both in my current Epirus game.

What are the conditions?

Just cycled thirty odd turns of my end game Macedonia with nothing popping in Alexandria. Had other tier 3 commerce buildings come up.

You need, if you are not the historical nation to wait 269 BC for the Light house. The coliseum should be buildable as soon as you have 6 culture buildings in the region.

Must just be unlucky then this was 150-110BC, lots of other tier 3 commercial buildings came round on rotation.

How do I get the Colossus? Should it be built on Rhodus Island?

Yes on Rhodes. If you start as them you'll get an event chain to build it. first step is either to drive off a siege from or import copper to Rhodes. Second stage is to reach glorious government.

In the alternative you can just build it normally - need 6 commerce buildings to be able to build Tier 3 buildings.

I disbanded most of the navy, fleshed out the army then conquered the rest of your starting province. Culture ratio quickly got me up to glorious, and it's just a question of hitting end turn/refresh buildings till you get it.

If you are not Rhodes, then 25 years after the historical date (which is the exclusive period for Rhodes to try building it) then everyone can try building it the regular and costly way. So it can be erected even in Sarmatia in theory.