For Apollo 11, why couldn't they use a colour video camera for the surface?

Read and learn:

http://www.clavius.org/tvqual.html

The LEM was battery powered. "Engineers had to keep the power requirements of the radio transmissions to the bare minimum so as not to exhaust the LM's batteries too quickly."

Just doing some reading on it. Apollo 11 had a color TV camera on board for use inside the command module, but it wasn't adapted for use on the lunar surface until Apollo 12. For TV pictures on the surface of the moon, they only had the slow-scan Westinghouse Apollo Lunar Television Camera. They had color cameras for taking still pictures, but all the color videos you see from the moon landing were from later missions (Apollo 12, 14, 15, 16, or 17).

Edit: Actually Time Keeper's link gives a much more detailed explanation. I can't verify whether the camera worked on the lunar surface or not. What his link explains, though, is that Apollo 11 also had the problem of transmitter bandwidth. It takes a lot more power to transmit a color image than a BW one. The Apollo 11 LM didn't carry a high-capacity antenna like they did on later missions. Also, because of delays in getting out of the space craft (it took Buzz and Neil longer to prepare for their EVA than planned), the receivers on Earth that were intended to pick up the first images broadcast from the moon (the ones of Armstrong getting out of the LM for the first time) were on the wrong side of the planet, so they had to settle for a weaker receiver in Australia. This reduced the usable bandwidth by even more, so all they could do was make the grainy, low-resolution image you see.

The command/service module had a high-gain antenna that could transmit color images. The LM did not. On later missions (Apollo 12 and onward) they deployed a high-gain antenna after landing.

A color camera would be very large and heavy and consume a great deal of energy which was sparse on the LEM.