Co-Ops that accept non-US permanent residents

Not sure there's a written rule.
When I bought mine, the application form only asked whether I'm U.S. Citizen (I'm not).
Instead of the board, the bank will probably ask more questions about your visa situation.
So if the bank feels ok to loan money to you (a foreigner), I'd image the board should be ok too.

That's a really thorny question because immigration status IS a protected class under NYC Fair Housing Laws, but some co-ops seem not to have gotten the memo.

As a practical matter, when you do end up navigating the co-op process, show as many ties to the U.S. as you can.

An example: I had a co-op buyer who was a foreign national because she was born overseas, but she had been educated in the U.S. since nursery school, all the way through college. She worked for an international firm that had her on a work visa, in a fairly international job, so I figured one shadow in the board's mind was, "well, what if she wants to go back to her home country?" and another shadow in the board's mind was "well, why wouldn't her employer transfer her to another fairly international city in four years?"

So for our application, for recommendation letters, we had a reference who was her roommate at her American college, who said something like "we were different because I grew up in California and applicant grew up in Virginia" (basically positioning her home country as here), and another from someone in her firm who basically indicated "they want her in New York because they're grooming her for big things here."

Does that help?

ali r.
{upstairs realty}

The coop needs to know that they can come after you for assets and get them if you don't pay. That's a lot harder when you can pick up and leave the country any time you wish. Exporting a judgment is costly and time-consuming even in the best of times. The presumption that you can leave and take your assets to defraud the coop as a creditor is a hard presumption to rebut. Why not just look at condos or townhouses?

One City Point.
https://streeteasy.com/building/brooklyn-point

@george, and yet co-ops are sold ALL THE TIME to people so wealthy that getting a judgement against them would be "costly and time-consuming," to put it mildly.

Indeed. My views on coops have been shared before. But it is harder for Americans to hide assets. A Cook Islands trust only offers so much protection. Much easier for a wealthy foreigner to slip away.