A rain barrel sounds more practical or multiple rain barrels or a water collection system.
I installed one for a client back in 2011 with a float valve that would fill it from domestic water when the water level dropped too low. I have a jet pump that pulls the water out and into the zones which are operated by a digital irrigation timer. The fill valve is opened and closed by the float valve and a mechanical timer that is in the "on" position so will apply voltage to the valve when the float valve switches it via the receptacle. Sounds complicated but it's just a matter of plumbing everything correctly and setting up the valves, etc.
(Timer which operates valves for each zone)
(Float valve which hangs down into the tank and plugs into a 110v receptacle)
(The float valve plugged in with the mechanical timer piggy backed on it)
(The mechanical 110v timer which operates the fill valve (see below) to keep the water level up to a minimum in between rain events. This line is tied into the domestic supply line.)
(The reservoir tank which catches rain water. Note the float valve wire through the grommet on top.)
(The top pipe is the fill line - the bottom is the output line plumbed into a small 1/2 HP 110v jet pump)
(The jet pump (Pedrello with a Pressflo pressure switch) which sends water out to whichever zone is opened at the time via the timer in the first pic)
We also have an inline filter to help keep the water quality clean to prevent clogging the irrigation nozzles. Two of the 4 zones are drip tubing and the other two zones use rotary nozzles which are great with low pressure systems.