Depends upon the magnitude of signal voltage. The peak magnitude of gate current should be limited to less than 2.5A for IR2110. You may want to limit it to 2A for all practical purpose.
So suppose if the signal voltage is 12V, the series gate resistance should be 6 ohm. Since IGBTs have an internal gate resistance typically between 1 ohm to 3 ohm, use an external 5 ohm resistor in series with the gate. (Check for the typical value of internal gate resistance of FGA25N120)