You would build two of the attached, one for the green one for the blue side... Resistor value to be determined when the power supply is chosen, and will slightly vary from blue to green... Power supply should be 16V @ 750mA minimum to give a little head room, a little higher voltage won't hurt but don't go too high as it's a waste, although if you want 5 LEDs a cup you will need about 19-20V as a minimum... The mA rating can be higher and it won't hurt anything, and technically could be as low as 500mA but I wouldn't go that low...
Look on Ebay at laptop power supplies, you will easily find one in the 16V-18V range with plenty of mA for this project, and they are low cost...
Example
http://www.ebay.com/itm/64W-AC-Powe...03303?pt=Battery_Chargers&hash=item2c6881e147
Remember that would only power 4 LEDs per cup...
Once you have a power supply chosen, then it's just a little math to work out the resistor values...