My thought was that decaffeinated coffee should be gluten free but when you add a creamer or sweetener that can change things considerably so you would have to read the labels on those things you might add. Knowing the sneaky ways that manufacturers get around things with fancy names for ingredients like if you see "Hydrolyzed Vegetable Protein" translation is "Wheat Flour"found that after long searches.
To be sure do a search on "Is coffee gluten-free". I found a site that gives all the answers to what you need but am not allowed to give other sites in my answer to you.
Good luck, keep questioning and read labels.