Sponsor/ Co-op Unit Owner Liability Insurance?

As a Sponsor in a small co-op where I still have a few units subject to rent stabilization and rent control, it has come to my attention that the co-op’s insurance policy will not cover a liability claim from one of my tenants should they be injured due to an issue within the unit. I would assume this applies not just to Sponsors but to any co-op owner that rents their apartment out. It seems that the insurance companies are double-dipping here because if the building is all rental, the building owner would be covered for liability even inside an apartment and yet the premiums are basically the same for a rental building and a co-op. I got a quote on a pure liability policy for the Sponsor units and it is about 80% of the cost of the co-op’s policy which covers way more than just liability! In any case, how do you other Sponsors and co-op owners that rent handle this? BTW, if you are tempted to suggest that a rental condition be that the tenant must purchase renter’s insurance, my stabilized tenants rent under leases that have been in effect for a decade or more and I cannot modify the terms at this point, so that won’t work.