If the guy responsible for the Willys custom also made Boston Blackie's car, it was C. H. Peterson.
Yes, C.H. Petersen is what I was looking for; not because I think he built the Boston Blackie car but simply because somebody thinks the car from the TV series is the Willys that he built. It's even captioned as such on his site! There are resemblancies but it clearly isn't the same car, and it's very unlikely to have been modified into the TV car because these pictures show what it looks like now, and I can't imagine anyone would have returned it to its original appearance.
So we're left with the popular solution that it's a modified Muntz Jet, though I have no idea who did it. Not C.H. Peterson as far as I know. Personally I'm not 100% convinced but unless someone comes up with some definitive proof of it or of something else it's all we've got.
Wendax already had a point for correctly identifiying the Boston Blackie car and I promised another point for identifying the builder of the Willys, so since Wendax provided the full answer he gets that one as well! Sorry oko94.