I looked for a serious answer to the OP's question.
In North America you can sell voluntary, certified carbon offset credits through the
Chicago Climate Exchange, if your carbon project offsets more than 10,000 metric tons of CO2 emissions. Each metric ton of CO2 offset is worth around $4 on the exchange. Certification would be done on a case by case basis as an energy efficiency and fuel switching project. I couldn't find any existing bicycle related carbon projects so you'd have to sell the idea to the exchange, obtain their certification and pay their fees.
I guess the obvious question is how many metric tons of CO2 offset could be credited to an individual living car free.