According to scientific studies conducted by organizations and associations on issues related to gluten intolerance or celiac disease, coffee has no gluten. However, you should be very careful with flavored coffee, which may contain gluten. Barley coffee on the other hand contains gluten.

Despite these findings, individuals intolerant to gluten have reported to have had issues after consuming coffee and prefer not to consume it. Below there is a list of types of coffees that are certified as "Glutenfree":
https://glutenproject.com/certified-gluten-free-coffee