Wow, are people really recommending mustangs as mustachian family cars? Don't those have huge engines, horrible mileage, cramped back seats, and no trunk space? May be I'm just new to the forums and too much of an idealist, but I think you can do much better.
My background: I like practical hatchbacks and stick shift too. My brother had a tercel for years, most economical car in the day. He drove it into the ground and it saved him tons of money. I had a 96 civic hatchback (stick shift) that got 40-45 mpg and could carry a dozen moving boxes. I had a single friend with a Miata that he let me drive, it was really sweet and I kinda wanted one too--so I totally understand. After a Subaru Impreza wagon that was reliable but only got 25mpg, I have the Nissan Leaf now because I wanted electric, but really it's just a 4-dr hatchback.
Let's start with convertibles: no matter how nice they might be, they have serious drawbacks, and I've never seen one that could be considered a family car. It just seems they don't have any space in the back seat or trunk, let alone 4 doors. That doesn't seem practical for shopping trips and weekends (then again, maybe your family doesn't pack up the tent and sleeping bags and go camping on weekends). Most of the ones mentioned are gas guzzlers: wranglers and mustangs have 5 liter engines. The article about the convertible Marano brought up the issue of visibility and I'd add safety (no roll cage, except in the wrangler). Then there is the issue of extra repairs if the convertible roof ever leaks or gets torn. And you don't mention where you live, but would you really use it? Because if there is any chance of rain, bugs, or even too much heat and sun, the top will tend to stay up all the time, and then you have all the downsides and no benefit.
Frankly, I'm of the school that a good family car is a used 4-dr hatchback, maybe a ford escort, Honda fit, Nissan Versa, or Toyota matrix. If I didn't go electric, that's what I'd have--my Leaf is really just an electric Versa. You should be able to find a decent one of those used for 6-8K and fill all your driving needs and save a lot of money in the long run.
Now, if you really dream of zipping around in a Miata with the top down, like I said, I can relate. They appeal to me because they seem to have that ideal design to fit that niche, and a used one isn't too expensive. It would obviously have to be your second car after the reasonable family car. That said, to keep it mustachian, it really has to be your hobby splurge, that one special thing you indulge in knowingly and lustfully. Buying a Miata as a play car while having other expensive toys or habits (say an expensive gaming rig with the latest titles, or a kitchen remodel) would seem like a frivolous excess if you're saving for FIRE (I don't hand out punches because I'm a pacifist, so I'll leave that to others).