Centre-back Goodison came off with a groin strain during Tuesday night's 1-1 draw against Notts County, while playmaker Robinson sustained a hamstring injury.
They join on-loan Stoke striker Mamady Sidibe (hamstring) on the sidelines, while skipper James Wallace is out for the season after undergoing surgery on a medial knee ligament injury.
"Goody felt a bit of a pain in his groin on Tuesday and he'll miss Saturday," said Rovers boss Ronnie Moore on the club's official website. "He'll be a big miss for us.
"Andy Robinson will be out for two weeks and Mama will miss Saturday too. So you've got three lads missing with all that experience and you're going to miss those type of players.
"James had an operation on Tuesday so that's him finished for the season. Pieces of both ends of the ligament had come unattached so they've had to reconstruct that."