I don't know the date that the tower was constructed, but it has been a dominate landmark in the Kerman area for many decades.  On a clear evening its red warning light beacons can be seen from Fresno.

KMJ used to transmit from Kerman from 1941 until a year or two ago.  KMJ was 5000 watts non-directional day and night.  KMJ now transmits at 50,000 watts directional (signal beamed to the West) from a four tower facility just northwest of Orange Cove, California.  KMJ has retained the Kerman facility as their back-up transmitting location and the tower is over 600 feet tall.
 
KMJ moved to Kerman due to the construction of Hammer Field (Fresno Air Terminal) in 1941.  The KMJ transmitting facility was previously located on the corner of Clovis Avenue & Kings Canyon Road where the Sunnyside Bowling Alley existed.  KMJ's tall Fresno tower was in the landing path of Hammer Field and the War Department paid for the relocation.
 
The Kerman site included and thick concrete underground bunker that housed a small broadcast studio stocked with emergency food and water and a back-up generator.  That "hardened" site still existed in the early 90's when I visited the facility with KMJ Chief Engineer Joe Mauk. 
 
Bob Souza
Former Fresno Broadcast Engineer
Roswell, NM