First of all, are you using a black and white TV? They made those once a upon a time, and if you're a kid maybe you have parents with an awesome sense of humor.
It sounds like you ruled out the game cartridge, so now isolate the issue to the console, cable or TV.
Plug your console into a different TV with the same cable to rule out your TV hardware.
Plug your console into the original TV using a different cable to rule out your cable.
Try a different type of cable (RF, composite, s-video), and if one of them gives color while the others dont, maybe you can work around the problem instead of fixing it.
If using an RF adapter, are you using the correct/same channel (3/4) on your TV and the RF box?
If you're using an S-video cable, maybe you're only getting luma and not chroma?
There should be 4 metal pins and one plastic guide tab in an s-video connector, check for those being bent/broken.
If SCART or import hardware... well I hope it's not an NTSC vs. PAL issue. Google for region-specific issues.
I just fixed my SNES with this problem, monochrome output on composite and S-video. Occasionally some color would appear. It was due to the master clock crystal frequency drifting slightly with age. To fix, use gamebit driver to open SNES case, remove just screws holding metal shield over circuit board (leave power switch in place, as you don't want it shorting with board), then reconnect SNES to TV and put game in, power on, observe monochrome output, then slightly adjust the small screw in the red component near the front. Mine had to be turned slightly counter-clockwise, but try both directions. Find point where color just fixes, then turn about 20 degrees farther so that it's not just about to go monochrome again. This fixed the color on mine and now it works fine.