While he doesn't explicitly say the phrase "I Don't Do Mondays," he does express his dislike for Mondays in a very memorable way.
In the 1978 Peanuts special "It Was a Short Summer," Charlie Brown expresses his Monday blues by saying, "I hate Mondays. They're always after Fridays, and nobody likes Fridays after Thursdays."
This iconic line became synonymous with the Monday blues, making it a relatable phrase even if it wasn't directly uttered by Charlie Brown.