Photos would help, but if you are talking rigid frame, the angles of the tank won't match the angle of the frame. You would need to get a rigid style tank, or something custom. It could be done, but, IMO, would look mismatched.
Curious about this too. I have a Santee frame and nothing fits well in it. The frame is wider then normal and pops up just before the center down tube and leaves a void on top of the tank. Thought a softtail tank might fit better.
Jersey Thunder, I do have a brand new Paughco chrome horse shoe tank if you need one.
Here's a pic of a stock Softail oil tank, pre 2000 I think, in a Paughco rigid. Not a very good pic, but it's the only one I have and the bike"s stuffed in the back of the garage behind a bunch of other crap and motorcycles at the moment. The lines of the tank fit really well from the side, and there's plenty of clearance underneath for a starter motor if that's your pleasure.
I used the stock softail front mount with the rubber piece, but had to space it up from the frame tab. In the rear I sorta "hung" it from the crossbar. I used long bolts up through the oil tank mounts, through spacers, through the crossbar nutted on top, then the protrusion acts as the lower seat spring perches. It's a mockup and the rear mounting needs re-engineered, but it's sturdy.
From the top, the tank is wide. It sticks out past the frame rails maybe 1"-1 1/2" on each side. I saw somewhere that someone had narrowed one by cutting a section out of the middle. The battery compartment is wider than the battery tray, so there's room to narrow it and still use the same size battery, or maybe one slightly smaller, and still have enough oomph for the electric leg, if that matters to you.
Here's a '99-back Softail oil tank I did about 6 years ago, in not only a rigid frame, but a knuck repop rigid frame to boot. I mounted it same as you would the stock Softail tank, using the OEM-style hardware, and adding the corresponding rear mounting tabs to the seat crosstube. The '97-up Softail battery just squeezes between the frame rails in the battery box.
Only thing I did, was take the bottom oil line spigot tubes out of the Softail tank, and reconfigured the lines like a horseshoe tank would have them.