My neighbor is looking for a specific variety of plum tree. She says it's a Japanese variety with a greenish skin. I've been looking online for her and the only green plums I can find are gage plums. The closest to a green Japanese plum I've seen is Shiro, which is more yellow.
ume plums (Prunus mume) has greenish fruits with a sort of reddish blush. beautiful flowers, sweet tart fruit. used to make umeboshi pickles, which happen to be exceptionally delicious.
However, there are some varieties of Japanese-American plums, such as Elephant Heart or Satsuma, which could fit the bill, because they're sometimes greenish.