Once they start growing in the spring I'd water when the soil is dry an inch or so down. We're super dry here late spring all the way through summer so I end up putting down a couple of gallons twice a week via drip lines for each peony and that only wets the soil out 10" or so from the emitter on all sides. Make sure you don't let them dry out too much after blooming either—late summer and into fall is when the eyes form for next year and you don't want to set that back.
