This phrase appears to not be original Irish, although some have said it has been Irish and out of use for hundreds of years. Hollywood keeps it alive, along with the response, "and the rest of the day to yourself."
It was used in Theodore Cyphon, a novel by George Walker, published in 1796. The protagonist is greeted not long after landing on the shore of Essex, "Halloo! you teney" cried one, "the top of the morning to you. Have you seen pass a tall chap, in a light blue coat, with striped trowsers."