First, check the build cost of your designs is less than the shipping lines available funds.
Second build a freighter of your own and some infrastructure (build the infrastructure yourself from the industries tab) and move it to a colonizable world. I'm not entirely certain but I think that civ lines don't look at supply and demand contracts and decide to build a ship to fulfill them. Instead they need to see a situation that they can fulfill that is already present, such as available space for colonists on another world.
Yeah, I figured they might, that's why I put a population on titan, to spur them into doing something, but it didn't.
Uh, noob question, how can I tell how much my designs cost a company? I think that might be the reason (the design by this stage is pretty big for a start up company I guess), and I'd be happy to subsidise them up to the required wealth level, but I don't know how much it would cost them.