They had a half court on the Paradise but it wasn't open very often. You might want to check up by the shuffle board area when you board. My DH got a ship on a stick for being in the b-ball tournament.
We just got off the 3/23 Inspiration sailing a week and a half ago. There is a basketball hoop (not a court, though) one deck up from the lido deck in the rear of the ship in front of the snack bar by the "adult" pool. Believe me, our sons can spot a basketball hoop from a mile away, and they sure found that one (although they can't always spot their homework!). It did need a new net, though.
One of the ship activities was a 3-on-3 basketball tournament.
Oh, happy days! My son & his two friends, all 18 are sailing with my husband & me on 6/8 on the Inspiration. While girl watching & dancing are high on their lists, they were VERY disappointed when I told them that (I had been told)there was no basketball. Last year, on the PRIDE, my son's friend carried a basketball when he boarded *just in case* the ship didn't have one. They ended up building a mock goal!
AOS - 3/07
AOS - 9/05
NCL STAR - Alaska
NCL's STAR - Alaska 6/06/04
Sensation - W. Caribbean 2/21/04
Inspiration - W. Caribbean 6/8/03
Pride - W. Caribbean 6/02
NCL's Sky - Alaska 6/01
Fantasy - Bahamas 6/97
HAL's Zaandam - E. Caribbean 6/00
HAL's Ryndam - Alaska 9/98