MrGarak:
The board is the following:http://www.ebay.com/itm/USB-4-Channel-Relay-Board-RS232-Serial-controlled-/280879280954
As I said, it's an independent board with its own microcontroller. I would assume they integrate diodes on the PCB, it would be stupid not to. But who knows hm? The inductive load is a small motor, 1.55 amps, 120VAC.
As MarkT says, ideally you need to know the inductance of the motor to calculate the values for the snubber network. However, I suggest you try 0.22uF in series with 33 or 47 ohms. The capacitor needs to be rated for well above 120VAC, and the resistor should be rated for 500VDC or more. Something like http://uk.farnell.com/panasonic/ecqu2a224kla/capacitor-x2-0-22uf-275v-10/dp/1673311 and http://uk.farnell.com/multicomp/mcf-1w-33r/resistor-1w-5-33r/dp/9337849.