Coulter played mostly on the outside at the University of Rhode Island, Deepi Sidhu of the Texans' official site reports. The Texans selected Coulter in the fifth round (171st overall) of the NFL Draft.

Coulter was a three-year contributor during a college career that included seven 100-yard games. In 2019, he finished with 1,039 receiving yards on 72 catches and eight touchdowns over 12 games. Coulter played mostly outside because of the Rams' lack of wideout depth, but he feels he can play inside. "I feel like I could play inside or outside," Coulter said. "I would just have to lock in and learn the plays from different spots on the field, but I feel like I could play anywhere." It's unlikely Coulter will make an immediate impact on offense, which includes six veterans ahead of him on the depth chart, but he will have the opportunity to learn from them during his first year as a Texan.