I assume you mean carbon dioxide credits, not carbon credits. Because for fireplaces it would have to be actual carbon credits - fireplaces release lots of carbon into the air as pollution.
Incidentally people should stop being lazy and say carbon dioxide when they mean carbon dioxide - otherwise it gets confusing in situations like this where fireplaces release both carbon dioxide, and carbon, into the air.
I specifically meant carbon credits. E.g. price of, for example, wood burning stoves could build in a fee/tax charged to manufacturers or importers given the nature of the product.
It's not just the air pollution, it's also cutting down trees, though at least when we cut it was usually clearing farm land.
As for existing fireplaces/stoves, I suppose a tax could be levied if they are the primary heat source. There are already lots of incentive based energy efficiency city and statewide programs around the nation that factor in heating method (and a lot of people eyeing the carbon credit "mining" in that case as well).
You're actually thinking about carbon dioxide (CO2) and carbon monoxide (CO). Carbon is just the atom (C), and both carbon CO2 and CO are carbon-based molecules.
Incidentally people should stop being lazy and say carbon dioxide when they mean carbon dioxide - otherwise it gets confusing in situations like this where fireplaces release both carbon dioxide, and carbon, into the air.