I have had ice cream at the Sweet Cow in Lafayette lots of times and have never gotten sick. There is no dedicated GF menus, but they do list the allergens for all the different ice creams on their website. They don't have dedicated GF milk shake mixers, so be careful of that. The quality of the ice cream is simply outstanding.
Based on reviews, we went in for ice cream, but were told they do not have a dedicated gluten free machine (as mentioned in a review) and all ice cream is made in the same machine. They couldn’t tell us which ice creams were gluten free and all they had was an allergen list with wheat on it. We decided to pass. Very sad because we used to love sweet cow.
When I told the staff that I was gluten free they immediately got a new scoop for my ice cream. This is the only place that has ever happened, and they have separate ice cream makers for gluten dairy free paleo and vegan\vegetarians. And everything tasted delicious. I also have some friends that have celiac and they only eat ice cream here. I just love this place!