Is there a substance that will eat through and completely dissolve carbon but not damage engine cylinder, piston nor rings?
If it's pure carbon, then the only way to remove it I can think of is by rigorous oxidation (e.g. by burning in oxygen flow or by reaction with strong oxidants (e.g. conc. $\ce{H2SO4}$, $\ce{HNO3}$)), but this is going to damage the metal parts either, as Ivan said. 

However, if the clog is caused by soot and resinous residue from the incompletely burnt fuel, then most likely hot toluene or xylene can dissolve the residue and liberate the carbon particles. Both are widely available solvents which won't damage the metal parts (but avoid contact with rubber tubing) and are also used to remove clogs caused by paraffin wax.

P. S. Both are highly flammable liquids, so do not warm them up using an open fire (e.g. use an improvised water bath)!