I use a standard press board case for my Boucher (Sam Ash - ~$40). I've never really had a problem, other than I would love it to be more waterproof.
My gourd banjo is a bigger problem. I presently use a soft sided guitar gig bag. I've toyed with the idea of making a custom case, but figuring out the materials is sort of an issue. I built the gourd banjo, and it is possible that the case will end up costing me more than the banjo did.
For my Boucher style (and my other 19th c. banjos), I use one of several gig bags meant for electric guitars (much better use, don't you think?
Which one I used depends on what else I'm carrying to the gig. I don't fly with instruments anymore -- don't get me started with that! When we don't want to drive to a gig, we take trains and in that case, I'll put several instruments in a trunk separated by foam and blankets.
I've been considering alternatives lately, so I'm quite interested in what you all have to say.
I had a nice period coffin case, but it went with the Sweeney I sold. It was nice, but mostly went unnoticed at gigs and the esthetics gained were not worth the tradeoff of limited protection. With the Boucher I have now, I am looking only for solid protection. Gig bags are okay, but always pressure the pegs too much. I think I will be okay with a slight retrofit on a HSC, possibly removing the center compartment and modifying it for neck support would be good. I suppose it will need a slight bit of foam or something to reduce rim gap.
I'm presently designing a case for my gourd. I've given up on looking for commercial cases. I've a design in mind. I'm planning on using 1/4" plywood. There will be some framing and foam inside. I'll use some thin aluminium angles on the outside of the case, with ball corners. I'm still working out the details, but I'll keep you posted.
I think I found a good solution. As a retailer, I made pretty good search for cases, as quality gig bags have been a problem in my business. I found a source, and had them send their banjo bag with my other order. It is a perfect fit for a typical Boucher, and offers good protection for light travel (non-airline). It has a stiff support, where most gig bags are too soft and lack protection.
I will post some pictures later. The brand name is ACCESS.