I would consider service_times:sensory_friendly= . as it’s a variation on the service_times:*= for such services. But sensory_friendly:service_times= means the times when the feature is sensory-friendly. Regardless, I prefer *:conditional= to have =designated for permanent sensory-friendly facilities.
service_times:*= has already been used for some languages Search results | OpenStreetMap Taginfo
A service_times:*= was part of a vote, in the format of ramp:wheelchair= Key:service_times:wheelchair - OpenStreetMap Wiki
For illustration, eg sensory_friendly_space= might be used whether there’s a “quiet room” / “sensory room” / “calm spaces” in a facility. Then sensory_friendly_space:opening_hours= would be used for the opening_hours= of it. However, I would consider this together with general resting spaces. Lounges in airports, train stations etc - #44 by Kovoschiz