Using a CFL ballast to power 9W UV tubes
This is a UV B (365nm) lamp with two pins. A bi-pin tube is designed for conventional (inductive) ballast and is incompatible with electronic ballasts. Internally it has a capacitor that acts as built-in starter.

You can connect it with single ballast rated at approx 9W (usually one ballast covers range from 5 to 11W). In your case you would have to connect 3 or 4 bulbs in parallel (ballast is a current shift component) and ballast in series. However if the ballast has 4 pins it means it's designed for 2 x 16W load, so you could connect just two bulbs to one terminal (this is close to 18W). You should check (with ohmmeter) if there are actually two coils inside. Connecting four lamps will slightly overload it (you would need a 36W ballast for that).

Personally I would try connecting two bulbs in parallel and then hook those to one half of the ballast (ballast goes in series with the bulbs). This would give the current flowing thru the bulbs a proper cos(fi) and keep the load on the ballast under 20W.