Boyce joined League of Ireland club Derry City's under 17 side in 2017, making his first appearance against Dundalk U17 in July 2017. He played with the club's under-19 side in 2019, before making his senior competitive debut in the League of Ireland Premier Division as a substitute against Cork City later that season in September 2019. Boyce signed his first professional contract with the club in January 2021. He scored his first senior goal in April 2021, securing a 1–1 draw against Drogheda United. Boyce was voted Derry City Players' Player of the Year for the 2021 season and was also named in the 2021 PFAI Premier Division Team of the Year. Boyce made his 100th appearance for Derry City as the club defeated KuPS to reach the third qualifying round of the 2023–24 UEFA Europa Conference League. On 10 November 2024, he featured in the 2024 FAI Cup final as his side were defeated 2–0 by Drogheda United. On 6 December 2025, Derry confirmed that Boyce had left the club after turning down a new contract offer, having made 175 appearances during his 7 seasons with the club, scoring 15 goals.