Is it possible to use diatomic carbon to utilize a new type of fuel that takes away the waste product of carbon dioxide being released into the air?
No doubt, diatomic carbon does exist - in blue flames and in comets. 

The characteristic uv absorption pattern (Swan bands) has already been described almost 100 years ago.

At low temperature (77 K) it reacts with hydrocarbons by H-abstraction to form $\ce{HC#CH}$, and the addition to $\ce{C=C}$ double bonds has been reported too.

But I can't figure out any reasonable way for a reaction with carbon dioxide.