In normal operation, there's no need for a series resistor. To calculate a resistor that protects the opto triac under all conditions, including load short, apply ohms law. R = 250V/0.07A = 3600 ohm.
Unfortunately, the series resistor would reduce the load voltage in normal operation to 70% (assuming a resistive load) and must be rated with 18W to handle a load short. A dead end design idea, I guess.
Your only option is a small fuse to protect it (~ 50mA rating).
Adding a resistance will limit the maximum current but at the expense of dropping the voltage and creating heat. The MOC3062 is designed as a triac driver, a switch to drive a larger device rather than being used as a switch itself.
Read the note on page 7 of the data sheet:
"This optoisolator should not be used to drive a load directly. It is intended to be a trigger device only."
The difference is that when connected as a driver device, most of the voltage across it is shorted out when the main triac conducts. Theoretically, as long as you limit the current to well below 70mA (maybe 50mA would be safe) it should still work in your schematic but the only way to do that is to ensure the load can never pass more than that current. If there is a risk of more current flowing, you either have to protect it with a fuse or add a current monitoring circuit to cut the power.