The Hobart-born Paine represented Tasmania over 18 years after debuting in 2005, playing 153 first-class matches.
In the dramatic final over, Coyte bowled Annie O'Neil (28 off 20) off the first ball before getting South Australia skipper Jemma Barsby (28 from 17) stumped two balls later.
Tim Paine had quit after being investigated by Cricket Australia for sending explicit text messages to a female co-worker four years ago.
