Cousins probably won't do it as far as sponsorship goes. Normally, they want someone a bit closer - like parents, siblings or children.

While it's true there is no "retirement visa" per se, there are over 20 different sorts of (non-immigrant) visas, so chances are you can probably qualify for one of them, especially if you have taught (i.e. worked) before in the US. Or, given that they are looking for science and maths teachers, you might be able to take a "last job before retirement" in the US and score an immigrant visa that would allow you to stay for retirement.

Take a look at the US embassy website in the country you're currently living in. They generally can link you to all the official websites on visas and often the local staff can be pretty helpful. Or if they aren't, check the website for the London US embassy.