For some reason the pilot has to take off in an emergency or is on a runway too short or maybe they just want more places they can land and takeoff. The single engine plane is already light on fuel and cargo. Could adding Nitrous oxide or richer fuel or something like an afterburner for a piston engine work?
That really depends how safely you want to get off the ground.
If you are looking to get in and out of tight airfields using STC'ed parts you may want to consider a STOL kit which can modify the plane such that you can utilize a shorter runway.
There are some airframes that do have horsepower increase modifications available but that takes actual mechanic work and wont really be feasible in your "pinch" scenario.
There are a few aircraft that can be operated with JATO rockets and it looks like it was done at least once on an ercoupe during testing
You could add Nos but then again most pilots prefer their engine to run for the duration of the flight... You would also have to contend with the fact that adding NOS may very well require a direct port bore, which is no small job.
Most methods of increasing engine power would require major modifications to the engine which would require a Supplemental Type Certificate from the FAA. This would include the use of alternative fuels or fuel additives.
A better and much easier method to achieve your goals of shorter runway requirements is to reduce the aircraft weight. This can be achieved by carrying fewer passengers or less fuel. In certain extreme circumstances, you can also lighten the airframe itself by removing unused seats or even doors. But, it may make the aircraft unairworthy.