Overwater SAR was flown without autopilot, doppler, etc. in Canada for 35 years with only one incident that could have been prevented with computers. Lack of computers was not the cause; the incident happened due to a breakdown in cockpit communication/CRM.
A load of computers in the cockpit reduces the pilot's workload, but it is still imperative that the crew have adequate training and procedures.
It may be possible to have an extremely safe operation in a single pilot, single engined machine without doppler, autopilot, radalt, etc. as long as the pilot works well with the crew and the procedures are sound. However, it should be obvious that there are large holes in that operation. For example, what if the pilot sneezes in the hover? With that in mind, I think it's fair to demand a two pilot and one rear crew member operation. Extra safety is realized with radalt, doppler, and autopilot (in that order).
Survival and safety equipment helps after the incident occured. RUET (egress) training, EBS, survival clothing, WSPS, aircraft flotation systems, and survival kits are all good ideas (in approximately that order).
Other equipment that comes to mind aids in mission effectiveness, but not necessarily in safety. NVIS allows you to complete more missions, but if the judgement is so poor that the wrong missions are attempted without NVIS, then that judgement could still occur with NVIS. Weather/Search radar has obvious mission enhancement capabilities, as far as increasing safety it again falls down to understanding the limitations of the equipment you have.
ShyTorque's comments regarding response time and fatigue are bang on. There are many studies regarding fatigue due to dusrupted diurnal cycles. DCIEM may be a good place to start looking.
Two other areas that are worth mentioning, but must be treated carefully, are experience and background. Experience by itself does not ensure a safer operation. However, low time pilots don't belong in the more demanding environments. The skills that are required go well beyond 'stick actuator'. Judgement, leadership, understanding limitations, courage, etc. should be considered when hiring for the dangerous demanding missions. This is one area where the military background might have an advantage over the civilian background. While the civilians tend to develop the better hands and feet while gaining experience, the military focuses on procedural flying and discipline. I tread lightly here because I don't want to imply anyone is better than anyone else, just that different skills get developed. Also, don't ignore anyone's serious application for a position, a diverse pool could offer much more than hiring in the same image.
In short, don't rush to blame the pilot or the equipment. The system itself should first fall under scrutiny, especially when there is a surge of incidents.