I spent a while this morning looking at this but I'm sorry to say that I've come up with a big fat zero for the combination of someone called Walter Butler, a draper, with wife Mary (let's say surname = something... BTW, where did "Mary Eileen" come from?), who had a son William in Enniskillen around the mid 1800s. I've chased all the usual sources - Griffiths, Tithe Applotment records, PRONI wills, various Irish directories and newspapers, BMD databases, Fermanagh Gold, etc. - but to no avail. There was even a 1956 will for a Walter Frederick 'Buttler' of Stratford-on-Avon referencing Northern Ireland, but I couldn't see a connection.
For that mid 1800s era, there are a number of Walter Butlers in other Irish counties (eg. Galway, Tipperary, Kilkenny, Dublin, Mayo), some well connected (in terms of peerage), but the forename / surname combination is really not a common name beyond those specific counties, and not in Fermanagh.
There are some contemporary Butlers and Nixons in Fermanagh, but no obvious connections to a Walter.
Maybe William got his Enniskillen birthplace wrong (do the marriage record and daughter's birth record clearly say Enniskillen or qualify it with County Fermanagh?).
Maybe he got it right and parents Walter and Mary were just temporarily in Enniskillen (passing through).
However, absence of evidence isn't evidence of absence, hopefully fresh eyes will find something for you.
BTW, do you have any thoughts about the differing Butler/Nixon naming? Some of the times I've encountered this, it was someone illegitimate, I'm not saying this is the case here ...