When do you get the loyalty quest for Garrus in Mass Effect 2?

All loyalty missions excluding Legion's will be opened prior to obtaining the Reaper IFF (recommended doing all of the before starting this mission).

Kelly Chambers will notify you if any of your squad members want to see you (being their loyalty mission is now open) if you don't talk to them directly.

As you progress through the game's main story missions, usually around when you get to the point where you have to find the item to allow you to pass through the omega 4 relay is when all your squad mates begin to ask you for their loyalty missions.

Note: It's possible that any of the squad members could ask you for the loyalty missions even before that part in the game, but by the time you have to be able to get to the omega 4 relay is definitely when their loyalty missions are available if they weren't already.

garrus' mission doesn't come until later, after you recruit a few people in the illusive man's second set of dossiers..... if you want him to stay alive for ME3....get the ship upgrades, get everybody loyal suicide mission use a loyal tali or legion in the pipe have garrus lead both second teams have jack or samara (or morinth) create your biotic field send somebody loyal, that is not a great fighter back with the rescued crew (you must go thru the omega 4 relay at your 1st chance) take loyal people with you to the final battle, but leave good fighters to hold the line against the collectors

Just keep playing, he will ask you when you do a couple of missions.