I just went through that in my current game. They need 3 things.
1) They need at least 1000 credits to build ships. They start with 2000, which is actually plenty. Subsidizing isn't actually necessary until they have popped at least two ships. It takes 3-6 months after you meet all requirements before ships start to pop.
2) You must have a colony with infrastructure. This means you must build a freighter yourself. One unit of infrastructure is enough to start things, but it may take as many as 30 to really get things going.
-If they build a Liner, 1 unit Inf on a cost 2.0 planet is enough. However, I suspect there might be rounding problems with 0.01 pop worlds if your pop growth bonus isn't big enough. Shipping up to 5 infrastructure in this case may be necessary.
-If they build a Small Colonizer, then 15-20 Infrastructure is the minimum to get them to move colonists.
-If they build a Large Colonizer, then 25-30.
3) You must have Nuclear Thermal Engines. This means you cannot have civ ships until you have researched Trans-Newtonian Tech, Water Cooled Reactor, and Nuclear Thermal Engine, which can easily take decades. It took me 22 years to research these. Note that Conventional Drive ships are slower than some inner system worlds, and the AI isn't smart enough to plot an intercept course. I consider both of these facts to be bugs.
Until you research Cargo Handlers, you will get database errors every time they pop a new design.
Until you research Cryogenic Transport, they will only be able to pop freighters and luxury liners.
[edit]Edited for more detail[/edit]
