Did the 1960's have color tv?

Yes you could if you were in America. The US began colour broadcasting in 1956 so colour television was relatively common by that time.

In Europe, British colour systems only became available in 1967 although Germany began limited colour broadcasts in 1966, using the British PAL colour system. Although test colour broadcasts were being made in the mid 1960s in Europe, colour televisions were not available for sale at the time.