The only "green-skinned" Green Lantern from Earth was Jennifer-Lynn Scott-Hayden, aka "Jade". GL Wiki entry here, DC Wiki entry here.
As the daughter of the first Green Lantern, magical Green Lantern Alan Scott from the 1940s Justice Society of America, Jennifer-Lynn had green skin and a "power pulse" on her right palm that duplicated her father's Green Lantern power. So Jade was a "living Lantern", first becoming a heroine in Infinity, Inc.
Jade later lost her "power pulse", as it came from the magical Starheart, as did her father's Green Lantern power battery. Kyle Rayner found her acting as a supermodel in the 1990s Green Lantern run, and the two became lovers. When Hal Jordan time-traveled into Kyle's time, Hal Jordan as Parallax tried to kill them both, but was driven off. Kyle took a copy of Hal Jordan's older Green Lantern power ring and gave it to Jade to let her become the Green Lantern of Earth while he roamed the universe to re-start the Green Lantern Corps without Oa or the Guardians of the Universe.
Jade lost her Green Lantern power ring, somehow ended up in the Rann-Thanagar War where she was killed, and her residual Starheart power was transferred to Kyle, who became Ion before Rebirth happened to Hal Jordan and the Green Lantern Corps.
Jade later was resurrected by the White Lantern Living Entity during Blackest Night, and had her Starheart powers restored. At the end of Brightest Day Jade was with the Justice League of America before the universe was reset for 2016's DC Rebirth. Due to the story behind Alan Scott changing, Jennifer-Lynn and her brother Todd (Obsidian) were never born in the new continuity.
Jade has recently been resurrected again at the end of DC's Doomsday Clock run, but has not yet been seen in any other comics.