Cunningham was born and raised in Wagga. His father Mark played for North Broken Hill.[1] Harry played his junior football with Turvey Park.[2]
He was recruited by the club with pick 93 overall in the 2012 Rookie draft, before being promoted to the senior list in 2012. Elevated from the rookie list prior to the 2012 season,[3] Cunningham made his debut in the inaugural Sydney Derby, Round 1, against Greater Western Sydney.[4] In Round 15, 2014 Cunningham was awarded a nomination for the 2014 AFL Rising Star for his efforts against the GWS Giants.
In the opening minutes of the round two, 2024 match between Sydney and Essendon, Cunningham was on the receiving end of a crude bump from Essendon forward Peter Wright, which saw him substituted out of the match. Wright received a four-match suspension from the AFL Tribunal as a result of the incident.[5]
^The 2020 season was played with 17 home-and-away matches per team (down from 22) and 16-minute quarters with time on (down from 20-minute quarters with time on) due to the impact of the COVID-19 pandemic.