After initiating descent at center's request; B737 flight crew experienced dual bleed trip; which cannot be reset. Crew initiated emergency descent and diverted to the nearest suitable airport.

Narrative

In route at FL370. The flight attendants called to let us know that the passenger in 4C was complaining that the overhead 'blower' was blowing too much air and it was cold. Noted complaint. Center directed descent to FL340. Engine anti-ice turned on in descent. autopilot engaged. Cruise descent initiated. Right bleed light illuminated on descent passing approximately FL360. Reset bleed with trip reset; passing approximately FL350. Light stayed off for 10 seconds; then re-illuminated. Captain directed First Officer to turn off the right engine bleed switch as he reached for checklist. Bleed switch turned off; and shortly thereafter; the left eng bleed light illuminated leaving us with no pressurization available. Captain requested descent from Center and got descent to FL100. The intermittent warning horn inflight started to sound as we were descending. The Captain told me to put on my mask and initiated the emergency descent checklist. Oxygen mask; on crew communication established. As pilot flying with autopilot on; descent continued with speed brakes deployed in level change mode; near max VMO/MMO. Captain did the emergency descent checklist QRH. I was flying and talking to Center. There was a lot going on. The Captain interpreted the checklist to mean deploy the masks and told me was going to do so. I expressed to him that I did not think he should; but he said the checklist said to do so and deployed the masks. This was done passing FL250 in the descent. Captain told me to divert and I told Center of our intentions and set up for the approach. All items completed on approach descent checklist to new destination. The Captain notified Dispatch and the flight attendants of our new destination. Landed normally.