Flight Instructor with student reported the engine lost power during climb and they performed an off-airport landing.

Narrative

Took off of ZZZ about 103 temp outside; everything normal and in operating ranges. Cruise climb about 90 kts to maintain max airflow over the engine . Made it about 10 miles west to a climb altitude about 4000 msl; noticed a sudden decrease in fuel pressure while monitoring engine gauges ; engine started to loose power and we suspected vapor lock. Tried to troubleshot pumps; engine control unit (ECU) back up; fuel selector and cranking the engine over. Then tried to divert to nearby airport however couldn't turn on lights to see. Then diverted to road heading back into ZZZ landing. Didn't like the power lines and ridges on the road were hard to see as the valley now was covered by the shadow. Then diverted to the open area just off the right. Before touchdown full flaps; full aft stick; minimum controllable airspeed; canopy cracked in case of Airframe damage. Started clearing brush; bounced a few times then came to a stop in the sand. No injures sustained on landing; .we then secured the aircraft and exited to see if we had any leaks or fires for fuel. None noted; as well as airframe seemed to be in tact; no broken prop; wings hanging off; etc.