Interesting question but I would ask, when referring to "made today" does that mean in the same exact form as they were in 1951? If so, definitely not.
If they had some modern updates, well that would depend on what those updates were. I recently looked at some new Fiats and they have some similarities with the J - small, ugly/cute (depending on who you ask), economical, great colors and not a lot of cargo space (the J did have that advantage). Are the Fiats selling? We don't know yet.
If the J were updated with front wheel drive, modern suspension, power steering/brakes and decent transmission it would surely be more attractive but then people would have to ask "Why by a J when the Fiats, Smart cars and numerous other models are available?" Mercury, Pontiac, Plymouth, Oldsmobile, Saturn all went bust so my guess is, unless there is a significant price advantage (which there wasn't with the original) and it had comperable features (unlike the original) it would likely be flop today too.