Are you asking about a carbon road bike or an MTB?

If an MTB, carbon is still a high end material, and it's only in the last couple of years that mid range bikes have come out in carbon; also, given that the geometery of MTB's is still evolving, getting anything old will mean it won't ride as well as a new bike, standards a constantly changing as well, with hub sizes, headsets, handlebars etc all still changing.

You need to identify you riding type, bike type (rigid, HT / FS) wheel size (26" 29er or 650b) and budget, as all of these will have an impact on what to get, and even if any used bikes in that catagory exist