A Bb tenor case won't work without a lot of modification. I suppose it'd be possible to get a "form fitting" (i.e. "tenor-sax shaped") case and put a bunch of sponge or foam to "make" it fit.
Y'know, because C melodies are relatively common, your local repair tech might just have a decent one lying around. You also might be able to get one for cheap on eBay or ShopGoodwill.com. New? I'd assume someone has 'em, someplace. Aquilasax makes a C tenor now, but I don't know if that'll fit a vintage horn.