There is always a C wire, it is one side of the 24VAC and the other side is the R wire, but sometimes it is difficult to locate. I recommend getting a 16VAC or 18VAC adapter, and connecting it to the wire going to the thermostats RH terminal and a totally seperated wire going to the thermostats C terminal. That puts 2 wires on the RH wire which is OK.
Recommended C wire voltage 16V to 24V, AC or DC
Part # 802STA4116, specs 16VAC @ 250ma, about $11.00, phone 1-800 346-6873www.digikey.com
Part # T1129-P5-ND specs 16VAC @ 250ma, about $11.00, phone 1-800 344-4539http://www.mpja.com/18VAC-20VA-Plug-Tra ... /17560+PA/
18VAC W/Terminals and wall screw, about $4.00, phone 1-800-652-6733 http://www.sciplus.com/singleItem.cfm/terms/5103
Part # 27671 ADAPTER, specs 18VAC/100mA, about $2.00, phone 1-888-724-7587
17VAC doorbell transformer available at Home Depot