Lizzie,
Recently in a discussion, CA confirmed that there is absolutely no method to have zero downtime.
Echoing what Steve said, planning is the key to a near-seamless successful upgrade.
[Steve, was the first Instructor that I had a class with for Autosys when it was version 4.0]
The documentation links that are in the earlier post are definitely helpful, but there is no "one size fits all" solution.
This is from my actual experience with POCs, installs and upgrades
Depending on the set up of your environment, with proper planning there can be methods to reduce the downtime.
Good Luck!
Chris <CJ>