We haven't seen a mechanism or device that would keep PADDs or tricorders or phasers charged (and while the first two might consume so little power that they recharge from user movements or minuscule heat gradients in the environment, the latter are high output power devices). Perhaps such a mechanism is invisible? The idea of Data hooking up to it like any other toaster would appear natural enough.
Building a recharging mechanism into his cabin chair or Ops chair would also appear logical, but it wouldn't meet the criterion of him recharging "continually". If he recharged while aboard the ship (sitting, walking) but not while he performed away missions, this might still qualify as "continual" for the purposes of a discussion with a kid, as in ST:INS.