The American Heritage® Dictionary of the English Language, Fourth Edition (referenced at dictionary.com) has this to say :
Some speakers of vernacular English varieties, particularly in isolated or mountainous regions of the southern United States, use phrases such as of a night or of an evening in place of Standard English at night or in the evening, as
I moved to Southern Indiana (US) in 2001 and this phrase is common. "I will be at home of an evening" etc. Until just last night when I read a novel (from an English author) which used the same phrase I thought this was just "Southern" talk. It used to bug me a lot, now I know better, but it still bugs me