In England "of a morning" is standard, though not common, and is perhaps a little dated. It would be readily understood, and I don't pick it up as dialectal at all, though it might be more common in some regions.

"Of an evening he would go down to the pub and play darts." -- Or "He'd go down to the pub and play darts of an evening." -- yess, slightly old-fashioned.

Less commonly "of a night", "of an afternoon", but they're possible too. But "Of a Monday" doesn't sound right.