I bought Nuno's match worn shirt with his signature on his number on the back and the rest of the team on the front. It was from a mate who had a contact within the club. Cost me an arm and a leg but worth it. Framed and on my Everton wall alongside a lovely photo of the gorgeous man himself.b)
There's a few websites that have shirts, some are match worn but if you just want a shirt signed then I think it's just a case of hanging around and getting them to sign them one at a time.
I doubt the club would oblige but I may be wrong. They must have dozens of requests every week I suppose but no harm in asking.
The shirts look the business in a frame though. Also got a shirt with Pat Nevin, Sharpy, Duncan McKenzie, Leon Osman, Barry Horne, Ian Snodin and the wonderful Dave Hickson, also framed. Strange combination of players past and present but treasured nevertheless.