AFAIK the only thing that's required by law for private aircraft, day VFR is an altimeter, compass and airspeed indicator.
However, there are certification requirements for aircraft as well and these may lead to additional equipment. If so, then that's listed in the POH. Since the POH is the basis for the CofA, if the POH says something is required, then it's a no-go item if it's not serviceable.
I would imagine that aircraft who show a distinctive buffet before the stall, and have conventional stall characteristics, would not need a stall warner per se. But if there's no aerodynamic stall warning or otherwise, and nasty stall characteristics, a stall warner would be required.