Optoisolator Not Switching
The opto you used has a current transfer ratio (CTR) that is guaranteed to be 100% so, that's the good news but unfortunately to get 37.5 mA in the collector (to power the relay) you need 37.5 mA in the diode and its peak maximum forward current is only 30 mA.

However, it's a little more problematic than that because to push the opto-transistor into good saturation might mean the CTR reduces from 100% to 40% so you will struggle to get the opto-transistor to turn on hard enough to power the relay. See fig 11 in the opto data sheet.

I'd be tempted to add a regular BJT after the opto and then you'll only need to push maybe 5 mA into the base and this should be enough to fully activate the load. If you choose a BJT, come back and ask if it will do the job but you are looking for a BJT that has reasonable hFE at saturation (20 or more).