Would it be wrong to send an email to my CFM about a position that I am eligible for and I know is coming available?

career field manager

Oh, similar to Army Branch Managers or Career Consolers. Had I known that, I'd have answered "no."

Since the question was posted over a year ago, I'm sure the OP has moved on, however, the answer is indeed no, it is not wrong to send an email to your CFM provided that you have informed your CoC. It is better to have a SNCO do it, but that largely depends on how personable your CFM is and what rank they are.

It isn't wrong, but it might not get you what you want. In the bad old days, the AF Airborne Linguists were managed out of the HQ ESC/DOOR (later they were re-cast as HQ AFIWC/XOORA). Assignments had to be balanced against needs of the service, desires of the airman, skill levels, and personal inputs by Ops Supes, Ops Officers, and theater managers. When individuals made calls, they were just as likely to be brushed off as helped, depending on the situation in the air at the time.