The '64 Riviera A/C system used two identical dual-stage vacuum diaphragms. They are called "dual-stage" diaphragms because there are two "circuits" in each diaphragm. Vacuum applied to either port individually will pull the shaft in halfway. Vacuum applied to both ports will pull the shaft in all the way. You can test the diaphragm by putting a piece of hose on each nipple, sucking on it, and seeing if it holds vacuum. New diaphragms are available from Old Air Products.

The upper diaphragm is mounted on top of the heater duct.  It opens and closes the heater air door (not the heater temperature door, which is controlled by a cable).  The lower diaphragm is mounted on the bottom of the blower housing.  It opens and closes the recirculated air door.

• Unplug the wires from the blower motor.
• Remove the black plastic vacuum tank from the inner fender.
• Take the heater valve off of the inner fender.  You don't need to disconnect the heater hoses; just move them aside.
• Remove the blower motor from the housing.
• Remove the blower housing from the firewall.  This is the annoying part.  Two of the mounting bolts must be accessed from under the car.  I would recommend using a flexi-drive or a universal drive adapter on a socket.
• Pull the blower housing away from the firewall and turn it so you can get to the diaphragm mounting screws inside the duct.
• Remove the screw attaching the diaphragm shaft to the air door, then remove the two screws that attach the diaphragm to the blower housing.
• Reassemble and replace the vacuum hoses.

Don't forget to put a small bead of sealant around the blower box, etc. when you bolt them back to the firewall. 

NOTE: The vacuum diagram in the '64 shop manual (Fig. 11-80) is incorrect. The diaphragms are reversed; the one labeled "Heater & Evaporator Air Door Dual Stage Vacuum Diaphragm" is actually the "Outside & Recirculated Air Door Dual Stage Vacuum Diaphragm" (and vice versa).