If you have already formally renounced US citizenship, though, getting a visa or a green card is damn near impossible. You'll have to put a lot of money on the table to win that argument. The rules very strongly discourage deals of this kind, though that probably doesn't mean much any more if the last 3 weeks are a guide.
And regarding "a lot of money", we are talking Eduardo Saverin levels of wealth here. At that level, if you really really need to make the US your permanent residence again, you can make probably pull some strings and make it happen.
Have you, like, ever applied for permanent residency?
That being said, the green card lottery is apparently much easier if you're from Europe (because of the lack of competition for the 7% country limit of cards).
But overall, the US is among the hardest places in the developed world to get a good visa situation, I think.
Passport power?
Yes, and I'm sure after throwing away the US passport all it takes to get one from one of these countries is just asking them nicely, right? It's not like you have to spend years of your life living there or that your time has any value or anything.
Its complicated. If you don't have lots of assets, you are probably ok.
Are you eligible for Permanent Residency after renouncing US citizenship? I would have thought that such an action would have some consequences regarding future residency.
I remember reading this book about survivalism ("Emergency" by Neil Strauss--a really awesome read in investigative journalism btw), and he had a whole chapter on how to get a passport from St Kitts and Nevis. Basically, the point was that you need to buy property worth about a million, and if you don't get screwed over by real-estate agents or the government, you'll get it pretty quickly.
My main concern was that once you have it, it's not very likely that many countries would take it seriously. It's like a running joke that if you're a shady millionaire/mobster trying to dodge taxes and stash money away, you'd always have a St Kitts and Nevis passport.
And if you have a lot of money and want to get back in, an investor visa or even a green card is not that hard to get.