General aviation pilot reported while preparing to take off they had to taxi off the runway and into gravel to avoid a collision with a training aircraft that was landing on the opposite end of the runway without making any communication on CTAF.

Narrative

While operating out of ZZZ airport; we announced our intentions to take off via runway XX (a downhill runway); as is standard operating procedure for our crew due; to the size of DC3 and downhill slope away from the airport. Normal traffic pattern arrivals call for the use of runway XY. While ZZZ is a non-towered airport; there is a facility and airport manager who will sometimes provide additional services for arriving and departing aircraft such as advisory calls; weather updates; and parking information. As we took the runway after our CTAF call; the tower manager notified us that there was an aircraft on final who failed to make a CTAF call. Our aircraft had just lined up on runway XX and the offending aircraft was on at approximately 500 feet on final approach. Due to the opposite direction taxi; and checklist duties; our crew could not see the other aircraft until we were aligned on the runway. We made 3 attempts to contact the aircraft on final and tell them to go around. UNICOM did the same. The aircraft continued its approach and at approximately 300 feet when it became apparent that the aircraft was not initiating a go-around; the Captain executed an evasive taxi into the gravel and cleared onto the taxiway to avoid the landing traffic. The 172 continued its approach; landed and taxied clear. UNICOM then let us know that the runway was clear and we again announced our intention to depart runway XX. With no other traffic; we departed without incident. Upon recovery; the Airport manager notified us that the offending 172 was a student pilot with an instructor and they were on the incorrect frequency. Apparently; they never noticed the DC-3 on the opposite end of the runway and; because of the lack of radio communications; continued their approach.