Bobobie and Resinsoul both have layaways. I think you have to email in to Dennis and let him know that you want to do a layaway as the Bobobie site doesn't support it? Resinsoul has a section in their order form for layaways though so you don't have to email in to Sunny personally.
Impldoll has unlimited time layaways so you can take as long as you like to pay off your order through them.
Sugarble does layaways as well, their time frame is three months max, if I remember right.
Leekeworld does layaways for orders above $200, and it's either an option for a three-month layaway or a four-part layaway?
FDoll does layaways, 30% upfront and the rest when the doll is ready to ship.