Andorra, Liechstenstein, Luxembourg, Vatican City, Monaco, San Marino, Kosovo, Montenegro?
Moldova
Faroe islands
Malta?
Macedonia?
Armenia?
When you say appeared in the Premier League I assume you mean played a game. I can't remember if Nick Papavassiliou got a game for Saudi Sportswashing Machine or not, in which case would Cyprus be an answer?
Quite positive one of the two missing will be Kazakhstan...they joined UEFA not so long ago.
*edit* Second guess is Azerbaijan (just found a list of UEFA members).
Think Celtic came close to breaking it a few seasons back. The record should be Benfica's, surprisingly not Steaua or some Eastern Europe military clubs.
In the 60s, I'd imagine