How can I repair a leak in a PVC water line without bringing down the system for an extended period of time?
I would use Oatey “hot” glue it sets faster than regular but cost a bit more , only get a small can as it evaporates faster also. You can see the label most standard solvents require an hour or longer depending on the diameter , but hot glue is ready in as short as 10 minutes. Primers also help but hot glue doesn’t need primer or the orange stuff I use doesn’t. Also the air temp and working pressure make a difference, colder takes longer to set.

Added: most of the systems I have worked on are less than 80 psi I checked the lava glue I use (Oatey orange lava)  the sheet said 2 minutes assembly and cure but truthfully I think it is more like 15 seconds.  I have pressurized within 10 minutes , the chart shows an hour but that is for pipe up to 1-1/4” at up to 180 psi. 
I have done many repairs on 1” and below with just hot glue and had the water back on within 10-15 minutes of the last joint with out failure. I always tighten the lid and store on the lid the cab tends to seal that way but I usually have a brand new can available also.