I'm guessing you've already tried eBay and the other online auction sites... luckily there are several other options if you need a rebuild kit or carburetor for a CMX250.
The carburetor for the 1986 Honda Rebel CMX250 does seem to be a rarity, but sources such as bikebandit.com could offer advice, if not the exact part you're after.
And these sites look the best bet for Honda carburetors:
- motosport.com - currently offering a 20% discount on carburetors
- partsnmore.com - selling rebuild kits for the 1986 Honda Rebel carburetors for $16
- repairmanual.com - downloadable repair manuals for all makes of the Honda Rebel
- hondarebelforum.com - lots of support and advice here, it seems carburetor modification is quite an issue with Honda Rebel riders!
- oldbikebarn.com - a specialist stockist of old bike parts, with a section on the Honda Rebel CMX250
You might be surprised to learn that YouTube is a good place to look for motorbike mechanics help. This films comes courtesy of the Honda Rebel Forum people: