I'm pretty sure it's a made-up word meaning, essentially, "make sterile." I too was wondering about "steropoeic" (NOT "sterEopoeic") when I read it in William Barton's short story "Down in the Dark" (in _The Year's Best Science Fiction: Sixteenth Annual Collection_, edited by Gardner Dozois, c1999) and tried to look it up. The second answer from "Quizmonster" gives me the clue I needed when he/she says, "'...[P]oeic' comes from the Greek word meaning to make." "Stero" could mean "sterile" (I'm guessing here); compounded with "poeic" then "steropoeic" would mean "make sterile". This seems to fit the context in which it is used in the story...
A meteor has wiped out all life on Earth, and the only humans surviving are about 2,000 scattered across a few habitats and moons in the solar system where it's clear they won't be able to survive much past their own lifespans, so having children is just too tragic and not something anyone considers. An attractive woman is clearly trying to seduce the main character in the shower by displaying her body, and after some brief and mildly erotic description of that we read, "After a while, she looked up at me again, stretching her arms over her head, arching her back, flashing the red dot of her steropoeic implant." I think the implication here is that she's showing him, "I'm sterile, so it's OK for you to have sex with me."