The phrase is actually "*at* your (earliest) convenience". In your sentence, it's actually the "as well" that will need to be set apart to indicate a pause because it interrupts the train of thought, but in general, the phrase itself does not require a comma. i.e.: "Could you send me your hours {of availability?} as well, at your convenience?" "Could you send me your hours {of availability?} at your convenience?

Could you send me your hours as well, AT your convenience?