ZLC Center Controller reported they were unable to vector a departing air carrier away from a conflicting unidentified VFR aircraft because the air carrier was below the Minimum IFR Altitude.

Narrative

I was working multiple arrivals and departures into JAC. Aircraft X was released and departed IFR on the ALPIN3 departure procedure. Upon check in I noticed that I had VFR traffic at 12000 ft. about 15 miles southwest of JAC; and I called the traffic to Aircraft X. I informed the pilot that I could not give him any turns below the MIA; which is 12000 ft. in that vicinity; and asked him to do the best climb rate possible to try and top the traffic. I also instructed Aircraft X; leaving 120 turn 10 degrees right. I could not turn him further because of a 13000 ft. MIA box just to the west of the departure course. Leaving 11800 ft.; DAL reported the traffic in sight; but also that he was maneuvering in response to an RA. I responded; roger; advise when back on course. He maneuvered behind the VFR traffic and continued without incident.We cannot do anything about traffic that is 10-15 miles from JAC. We are unable to turn our departures due to the mountains; and this traffic is not required to talk to anyone. This is a relatively high traffic area for VFRs; and we have to way to control them. If we had an Approach Control at JAC; we could have MVAs instead of MIAs; so I could vector aircraft below the MVA away from traffic like this. Not sure if it is possible to lower the MIAs or make them more 'fine'/detailed to the terrain so we could turn departing aircraft sooner upon contact. Generally departures must fly 15-20 miles before we are able to turn them. If we made JAC a class C airport; there would be airspace where this VFR traffic was; so they would have to talk to us/Approach Control; or they would have to avoid airspace and would not be operating in that vicinity.