Wire 2 of the 120V windings in series. As long as it has insulation rating to handle the 240V it should be fine.
One use of such a transformer would be to stepping 120V (2 windings in parallel) to 240V center tapped. I'm still looking for one to do this that is integrated with an enclosure where I can put a 6-15R or C13. And I want to keep it small so I can carry it with me.
A very common transformer with 2 120V windings and 2 240V windings (commonly used to step 480 down to 120/240) would not work for me, since my goal is to get a center tapped output (120V or 240V) with a 120V input.
