No pre-orders, but you can sign up to be notified
It was announced last week that Mario Party 10 would be getting its own amiibo line. The good news is that every existing character in said sub-series (Peach, Yoshi, Bowser, Luigi, and Mario) would be interchangeable with the existing amiibo figures. In other words, you don’t need to double-up and buy both, with the exception of Toad, a brand new toy that will work with Captain Toad: Treasure Tracker.
In true Nintendo fashion none of the exact pre-order dates have been revealed, which is maddening when you consider that some of these sell out in 15 minutes. As a consolation prize, you can go to Amazon right now for Peach, Yoshi, Bowser, Luigi, and Toad, and sign up to be notified when they are available to pre-order.
Funnily enough, Mario is not listed yet, but he will be included in his own bundle when the game launches, so you should be safe if you really want the second variant.