Color video circuits can be done with discrete transistors, because it was even done with vacuum tubes. But it would not be simple.
Up to the conversion of the RGB signals first to color-difference and then to Y, Pb and Pr, would be straightforward (relatively), but I see a real challenge in actually performing the quadrature chroma modulation.
Again, it can be done. Not simple, though.
There is an excellent book on all the requirements: "Video Demystified" by Keith Jack.
Get yourself a copy, and pore over all the intimate details.