I searched around for the best bread maker with a gluten free cycle that had the highest ratings. I found these 7.
In addition to the gluten free setting, you want a bread machine with good consumer reviews, one that is easy to program and one that is easy to clean.
Here are the best options. Just click on the picture for reviews and sale pricing.
Cuisinart CBK-100 2-Pound Programmable BreadmakerCuisinart CBK-200 2-Pound Convection Automatic BreadmakerZojirushi BB-PAC20 Home Bakery Virtuoso Breadmaker with Gluten Free Menu settingHamilton Beach HomeBaker 29882 Breadmaker, BlackOster CKSTBR9050 Expressbake Bread Maker, White