I've read that capacitors are of limited benefit on serial coils.
On a parallel coil, you're completely removing the current path from the high-current coil when the EOS opens--and the coil resists a sudden change in current (super-high to none in this case), so it jumps the air gap. Capacitor absorbs that.
On a serial coil, you're elongating the current path when the EOS opens, so the current just goes from high to not as high. With not as large of a current difference, the coil doesn't react as dramatically and doesn't arc (at least not as much).