Lighting antique dollhouse

I’ve recently acquired a dollhouse made in Germany ca 1910. At some point it ended up in the US and someone added lighting. When I purchased it, the cord that plugs into the outlet had been cut and there was no transformer. The lighting system is a series power circuit system with 7 lights (1 in each room) with E10 screw in bulbs, 3 Watts, 250ma each. I purchased a transformer 12VAC/20VA and the lights do work, but barely, they are so low that it’s hard to tell that they’re on. What kind of a transformer should I be using to make the light up fully and without burning up the system? Thanks for your help.