Board Thread:Questions and Answers/@comment-27364860-20151215185702/@comment-24577221-20151215211959

It's only possible to breed a Rare during the special times that it's available. These are usually along the lines of "This Friday noon to Monday noon, Rare X and Rare Y are available for breeding!" Occasionally there are longer periods, or times when more than just a couple of them are available.

They're now available to buy in the Starshop at any time, using Starpower. That's quite a new addition to the game.