On the positive side, a lot of Greater Manchester libraries use the same IT system now, under a joint project. Oldham and Rochdale, I think Stockport and some others. And I'd bet a lot of librarians would see value in getting information out there.
On the negative side, I think that development has been a bit slow from the data interrogation side, so open data may be a way down their priority list. And, inevitably there will be a cost involved in setting it up- is there the demand?
You might find some basic longitudinal data (aggregate book loans, footfall and maybe others) is available via CIPFA, LGInform and local performance reporting (which will tend to be monthly/quarterly but probably hard to extract). Footfall is always dodgy though!
Martin