Does any species, in any age, in any of the works by Tolkien have designated days of celebration, except birthdays, besides the holidays mentioned in the article about the Middle Earth Calendar on Wikipedia?
Appendix D to The Return of the King lists the holidays from the article you linked above, namely three Lithedays (roughly Midsummer) and three Yule days (Midwinter). It goes on to mention that during the reign of Elessar the calendar was reordered, to commemorate the fall of Sauron on March 25th, and September 22nd, Frodo's birthday, "was made a festival, and the leap-year was provided for by doubling this feast, called Comare, or Ring-day." (Return of the King pg 447)
It is worth noting that April 6 is listed in Appendix B of the same book as being when "The Ringbearers are honored in the the Field of Cormallen" and the next year as when "The mallorn flowers in the Party Field." November 2 is when Gandalf and the Hobbits "come to Bywater and rouse the Shire-folk." (Return of the King, pg 430-431)