Born in Leighton Buzzard, Bedfordshire,[4] Cunnington started his career with Barton Rovers during the 2005–06 season, in which he scored three goals in 22 appearances.[5] He started the 2006–07 season with five goals in 13 appearances for Barton,[5] before moving to Leighton Town.[4] After scoring three goals in 13 appearances for Leighton he finished the season with Hitchin Town.[4] Having made three appearances for Hitchin in the 2007–08 season he signed for Aylesbury United in September 2007.[4] After making four appearances for the club he returned to former club Barton Rovers, before going on to finish the season with Rothwell Town, making one appearance for the club.[4] Cunnington started the 2008–09 season with Stamford, before joining Barwell later that season.[4] With Barwell in the 2009–10 season, he struck up a strike partnership with Kevin Charley that saw the pair score more than 50 goals, helping the club win the Midland Football Alliance title and reach the FA Vase semi-final.[6]
Cunnington joined Conference North side Solihull Moors in July 2010,[6] and having scored 10 goals in 22 appearances for the club he signed for Conference National side Kettering Town for an undisclosed fee on 1 February 2011, transfer deadline day.[2][7] He made his Kettering debut on 26 February, starting the team's 2–0 victory at home over Newport County.[2] He only managed his first Kettering goal in the side's last game of the 2010–11 season, a 3–1 home victory over Southport on 30 April.[2] He finished the season with 14 appearances for Kettering.[2]
Having started the 2011–12 season with five goals in 13 appearances,[2] Cunnington joined League Two club Dagenham & Redbridge on loan on 24 November with a view to a permanent transfer.[8] His debut came two days later after starting a 3–0 defeat away at Accrington Stanley.[2] After making four appearances for Dagenham he permanently moved to the club upon the loan's expiration on 4 January 2012, signing a two-and-a-half-year contract.[2][9] He joined Conference side Alfreton Town on a one-month loan on 9 March.[10]
For the 2012–13 season, Cunnington signed for Conference outfit Tamworth.[11] He enjoyed a successful season, ending up as the Conference second top-scorer with 21 goals.[12] Cunnington signed for Conference rivals Cambridge United on a two-year contract on 10 May 2013, becoming the club's fifth signing in a week.[13] and was part of the team that won promotion to League Two via the play-offs.[14]
Cunnington then spent two years with Billericay Town before signing for Dartford on 2 August 2019.[17] On 8 October 2019, Dartford announced that Cunnington had left the club by mutual consent.[18]
On 21 November 2019, Cunnington joined his third team of the 2019/20 season when he linked up with Romford.[20] He left the club in January 2020.[21] and joined Hornchurch.
At the beginning of the 2020/2021 season, Cunnington joined Isthmian Premier League side Cheshunt. He scored his first goals for the club in a 3–1 victory away to Long Melford in an FA Cup First Qualifying Round tie, scoring 2.
On 6 November 2020. Cunnington signed for Cheshunt's fiercest rivals, Enfield Town.