[3] Peverley signed a one-year contract with Charleston Battery in the second division USL Pro on 16 February 2011.
[5] He was also included in the New Zealand U-23 squad for the 2008 OFC Men's Olympic Football Tournament where he featured in all 5 pool games and scored one goal against Fiji.
He retained his spot in the team and was named in the final squad to travel to the 2008 Summer Olympics[6] where he played in all three of New Zealand's group matches against China (1–1), Brazil (0–5) and Belgium (0–1).
[7] Peverley was named in a 15-man All Whites training squad for a 12-day camp for New Zealand and Australian based players prior to the 2010 FIFA World Cup.
[8] He was not initially named in the final 23 man squad to contest the World Cup, but was subsequently drafted in as injury cover for Tim Brown who fractured his shoulder in a warm up friendly against Australia.