Air Traffic Controller reported working an aircraft that encountered turbulence and strong downdrafts resulting in flight below the Minimum IFR Altitude; off course and towards terrain. ATC vectored the aircraft to an area of lower Minimum IFR Altitudes and the aircraft diverted to another airport.

Narrative

I had just arrived for my overtime mid shift. I sat down at sector XX and everything was normal until I noticed Aircraft X below the 16;000ft MIA (Minimum IFR Altitude) near the mountains. This isn't necessarily alarming as something like this can be attributed to the altimeter setting; rather than aircraft performance or weather. Upon noticing Aircraft X below the MIA I switched over to the ZZZ transmitter site as I thought it would have better coverage in that part of the sector. I issued the low altitude alert and the current ZZZ altimeter setting. After another minute or two; I informed the pilot he was still below the MIA. Eventually; I told the pilot to maintain a block altitude from 160-170 thinking he could climb in the block and that would keep them well above the MIA of 16;000 ft in that area. At some point; around the time I issued the block altitude; I noticed the aircraft off course as well and I asked the pilot if everything was okay. The pilot informed me that they had encountered moderate turbulence and strong downdrafts. I asked the pilot if he would like to divert to a nearby airport. I mentioned a few airports nearby. ZZZ1 was the closest small airport and I think I mentioned that as an option; as well. Eventually; the pilot kept descending. At one point I believe I noticed the aircraft at 12;500 ft in a 16;000 ft MIA. At this point there was some difficulty communicating with the pilot and I attempted to inform the pilot of headings they could fly to get to areas with lower MIA's. Because I hadn't received a response from the pilot I assumed he was out of range from my transmitters; due to his altitude and I was attempting to get another aircraft to go to the frequency that Aircraft X was on to see if they could relay messages. Fortunately; Aircraft X started communicating again and informed me that they had the terrain in sight and would like to go to ZZZ2. I provided priority handling on behalf of the pilot and provided vectors to areas of lower MIA's. I attempted to estimate the position of the aircraft on the overhead VFR sectional chart; so I could attempt to find the nearest obstacles and their altitudes. This proved to be more cumbersome than useful and I focused on communicating with the pilot. The pilot eventually decided to change the destination to ZZZ3. Fortunately; a colleague came back to the area and started to perform D-side duties and communicated the necessary information to PUB (Publication) approach.Recommendation:We need better tools to provide controllers with more detailed information. In this case; terrain was a major factor and something like Foreflight or Jeppesen would be an excellent tool to allow us to use ADS-B data to see a more accurate representation of the aircraft position rather than looking at my radar display and trying to guess where that airplane is relative to any obstacles.