Father’s Day presents some of the same challenges in writing as Mother’s Day. Like Mother’s Day, Father’s Day is written with a capital letter at the beginning of each word—and is written as a day for the singular father—not plural (fathers).
The “official” take on that goes like this (according to encyclopedias as well as the Chicago Manual of Style):
“Although the name of the event is usually understood as a plural possessive (i.e. ‘day belonging to fathers’), which would under normal English punctuation guidelines be spelled ‘Fathers' Day,’ the most common spelling is ‘Father's Day,’ as if it were a singular possessive (i.e. ‘day belonging to Father’). In the United States, Dodd used the ‘Fathers' Day’ spelling on her original petition for the holiday, but the spelling ‘Father's Day’ was already used in 1913 when a bill was introduced to the U.S. Congress as the first attempt to establish the holiday, and it was still spelled the same way when its creator was commended in 2008 by the United States Congress.”
So…Happy Father’s day to my father, my children’s father—and all fathers—regardless of whether it is written in a singular or plural possessive manner!