From The TV IV

Cousin Oliver is a derogatory term for the introduction of a cute kid to the cast of the show, usually late in a long running series in order to prevent the show from growing stale. The term refers to The Brady Bunch, which added the Brady kids' cousin Oliver for the final season of the show.

Other notable Cousin Olivers: Olivia from The Cosby Show, Andy on Family Ties, Seven on Married... with Children, and Chrissy on Growing Pains.