All you need is a resistor(actually two), a cap, a suitable mosfet that
can
handle the current and voltage(relatively easy to find for a few dollars),
and a diode for a snubber.

BTW, if ac is on the cap and not rectified you'll either want to add
rectification or go with a triac/scr version instead. Mosfets only work well
one way. I'm assuming the relay is DC since you mentioned an electrolytic
cap.