Center Controller described event when VFR aircraft; below MSA; declared emergency with engine problems and requested IFR handling; reporter issued non-RADAR IFR routing to requested airport.

Narrative

I received a transmission from an aircraft. Once the I determined the position of the aircraft; they advised me they wanted an IFR clearance to ZZZ and that they were having mechanical problems. I asked the pilot his altitude; they then replied they were at 150. I told the pilot that they were in an area where the MSA was 160. I asked the pilot if they could maintain their own terrain separation to 160. The pilot responded that they were unable to climb; and that they were declaring an emergency. I asked the pilot if they were in good contact with the ground; and they replied that they were. I asked the pilot if they could accept the non-radar routing above the terrain that they were approaching. I spoke with my supervisor and explained the situation to him; that he was an emergency aircraft and needed an IFR clearance back to his base due to visible engine leak on the number one engine. I cleared the aircraft to his destination. I gave the pilot many advisories of the current terrain and the peaks that were in the area. The aircraft was well above the terrain; however below the MSA. I would recommend that we should follow up on this with some refresher training involving aircraft in emergency situations.