Q:

How to do a Rapid Descent in a jet with inoperative spoilers?

So, let us assume you are in a simulator for your favorite jet plane, and the instructor gives you a LOFT (Line-Oriented Flight Training) scenario that goes as follows:

A normal takeoff and climb to cruise altitude, and perhaps thirty minutes of normal cruise flight
The non-recoverable loss of speedbrake (flight spoiler) functionality due to a mechanical jam, or some other malfunction such as the loss of all SECs in a FBW Airbus.
Another 30 minutes of time to deal with the first malfunction: run the checklists, plan and initiate a diversion if needed.
You lose normal cabin pressure for some reason, and have to conduct a rapid descent to get back to 10,000' and complete your diversion.

How do you execute the descent, considering that the rapid descent procedures for most jets rely on using the speedbrakes to achieve a high descent rate without overspeeding the aircraft?  To use the 737 QRH checklist for Emergency Descent as an example:

EMERGENCY DESCENT . . . . . . . . . . . . . . . . . . . . . .Announce
The captain will advise the cabin crew, on the PA system,
  of impending rapid descent. The first officer will advise
  ATC and obtain the area altimeter setting.
ENGINE START switches . . . . . . . . . . . . . . . . . . . . . . . . CONT
THRUST levers . . . . . . . . . . . . . . . . . . . . . . . . . . . . CLOSE
Reduce thrust to minimum or as needed for anti-ice.
SPEED BRAKE . . . . . . . . . . . . . . . . . . . . . . . . . FLIGHT DETENT
DESCENT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Initiate
Target speed . . . . . . . . . . . . . . . . . . . . . . . . . . . Mmo/Vmo
If structural integrity is in doubt, limit speed as much as
  possible and avoid high maneuvering loads.
Level-off altitude . . . . . . . . . . . . . . . . . . . Lowest safe altitude
                                            or 10,000 feet, whichever is higher

A:

The answer is actually quite simple.
FOLLOW THE MANUFACTURES PROCEDURES.
In some aircraft (I don't have a 737 flight manual handy) there is an altitude limitation if the spoilers are inop for just this scenario.  When the aircraft was certified, they needed to demonstrate an emergency descent (in the allowable time) without them, and that might not be possible from the certified ceiling. If that's the case in the 737, then descend to the max altitude with spoilers inop (assuming that you started above it).  
If there is no altitude limitation and no special spoiler-inoperative emergency descent procedure (I have never seen one of those, but there's nothing to say that a manufacturer couldn't have one) then you simply fly the regular procedure without spoilers.  The manufacturer had to demonstrate this during certification and it must have been acceptable at the time.
As rbp says, most of the time you fly Mmo/Vmo at idle power after you don the oxygen mask.  IF the flight manual/checklist says that you can put the gear down (some do) then you may, but I wouldn't otherwise.  I certainly wouldn't slow to gear speed (unless the manufacturer says to....  Unlikely in a jet like this) because you are decreasing the drag by slowing, and taking time at altitude to do so.

A:

Go to the top right corner of the envelope and stay there (point D in the sample below. Sorry, I don't have the 737 envelope at hand). Engines idle, speed and load factor as high as allowed.

If airframe integrity is not critical, lower the gear to increase drag, but expect to lose the gear doors.

A:

Whenever trying to rapidly descend, you always want to think drag!
Throttle to idle, lots of s-turns, (aileron drag), get down to gear speed, drop the gear, and lower flaps if practical.
A limited crabbing-like manuever (intentional side-slipping) would greatly slow the aircraft as well!
I'm sure that Terry will be here to recant us with a tale soon!

