Did you try the SNES on a different TV to see if it is the TV or the SNES that is screwing up? It sounds like you did, but it wasn't clear if that's what actually happened.
Back when everything was switching over to color TV from B&W some very smart guy figured out a way for the color information to be broadcast over the old black and while signal. This allowed people with only B&W TVs to keep their sets and still watch the new color programming. There is a chip inside the SNES and either a chip or analog circuit inside the TV which encodes and decodes this signal. Either one could screw up, but it sounds like the SNES is at fault because the TV is in color on other channels, and also because you tried the RF converter with the SNES.
More info:
For backward compatibility with black and white television, NTSC uses a luminance-chrominance encoding system invented in 1938 by Georges Valensi. Luminance (derived mathematically from the composite color signal) takes the place of the original monochrome signal. Chrominance carries color information. This allows black and white receivers to display NTSC signals simply by ignoring the chrominance. In NTSC, chrominance is encoded using two 3.579545 MHz signals that are 90 degrees out of phase, known as I (in-phase) and Q (quadrature) QAM. Mathematically, the combination of two sine waves 90 degrees out of phase with each other, with varying respective amplitudes, can be viewed as a single sine wave with varying phase relative to a reference, and varying amplitude. In essence, the phase represents the instantaneous color hue captured by a TV camera and the amplitude represents the color saturation.
Have you tried cleaning the connection on the back of the SNES that leads to the TV?