How To Safely Charge A 110V Capacitor
The voltage rating of the capacitor is not important here (so long as it is sufficient). The capacitance is important, and the voltage.
When you charge it from fully discharged, half the energy used ends up in the capacitor and half in the resistor.
The energy in the capacitor is \$CV^2/2\$, so a 10,000uF capacitor would have about 6.5J of energy. If you charge it through a 220 ohm resistor the initial current will be 36/220 = 164mA, and the initial power dissipation will be almost 6W. The capacitor will be 63% charged in R*C = 2.2 seconds, and will be virtually completely charged in a few times that.
If our resistor is rated for 6W or more, we're okay on power dissipation, however that is a rather large resistor if we only intend to briefly charge the capacitor and allow the resistor to cool afterwards.
If we look at some resistor datasheets:

The 0414 type will withstand a more than 5W pulse for 2 seconds so it's probably fine. That's a 1W rated (continuous) resistor. Other constructions of resistor and other suppliers may have different pulse ratings so you should refer to the datasheets, and avoid using parts that do not have pulse ratings.
Here is what the voltage across the capacitor and the power dissipated in the resistor look like as a function of time:

After 1 second, power dissipation in the resistor has dropped to 2.37W.
Other considerations include the maximum current you can safely put through the capacitor (film types in particular can be damaged by excessive current, but at 10,000uF it's probably an electrolytic type) and any limitations on the battery or wiring.
Edit: Here is a typical 160VDC 10,000 uF capacitor.

Rated ripple current is 7.8A RMS (continuous at 105°C) so it is certainly not limiting.