Station Eight - Ask Greg has a few tidbits.
It is possible they turned him down because he was in a coma until very recently.
Asker: How long has Guy Gardner been active as a Green Lantern?
Greg: Well, this is more complicated. Guy first became a Green Lantern seven years before Team Year Zero. Then came the coma. Guy then emerged from his coma in March of Team Year Zero. - #17729
But it appears to be some kind of personality conflict.
Asker: Why were Hal Jordan and John Stewart so adamant to cut short any discussion on Guy Gardner's induction in the Justice League?
Greg: They're not fond of his... style. - #15704
Then there is the absurd.
Asker: When the other Lanterns said "No" regarding Guy Gardner , was it because of his good looks, his chiseled abs, or because they knew his ring-slinging skills would make them obsolete? All of the above is an absolutely acceptable answer.
Greg: I'll stick with "Um."
They did eventually ask him to join though.
Asker: During the time skip, has the Justice League issue another recruitment?
Greg: I'm not entirely sure what you mean, but I think it's clear that they've added members, specifically Blue Beetle (Ted Kord, since deceased), Black Lightning, Green Lantern (Guy Gardner ), Zatanna and Rocket. The first three were inducted together sometime during the time skip, the last two were inducted together shortly before the start of Season Two. - #17474