supressing certain decay paths and enhancing others with interference In a scattering reaction, there are many possible final states for the products, each with different production rates. 

Question: Is there a way in which we could in general supress certain rates of products of the reaction and enhance others? can we
  use coherence and interference of the initial states to modulate such rates?

As an application of such possibility, i'm wondering if we could enhance the production rate of antimatter (for the purpose of the question, let's consider antihydrogen) by a few orders of magnitude by such manipulations?
 A: If I understand your question correctly, you wish to use quantum interference to observe phenomena that otherwise have a low probability of occurring? If so, exploiting this is well known and well established in quantum optics. For example, take phenomena that occur with coherently prepared atomic systems, such as Lasing without inversion, Electromagnetically Induced Transparency, Light storage, Coherent population trapping etc. 
In these phenomena, you indirectly control the probability amplitudes experimentally by tuning laser parameters (frequency, intensity) or atomic parameters (suppress Zeeman levels by magnetic shielding, increase atomic density etc).
There are also a whole slew of optical interference based schemes that are used to generate entangled states of light (or matter!). 
I am too lazy to provide references right now. Just woke up. :)
A: Antimatter is laboriously created in high energy scattering reactions. The only copious production is antiproton production which happens with high energy scatterings of protons on targets of nucleons.
Antihydrogen is hard enough to create and keep for a reasonable time for study let alone control it with higher order quantum manipulations. Wikipedia has a summary of production methods.
Thanks for the info @perplexity, I had not been aware of the quantum control field. Chemical and molecular level energies seem to be the field of possible control of scatterings in the manner envisaged, which are low energy, and not the large energies required for creation of antiparticles.
A: It's possible, but it requires that you make something happen before Fermi's golden rule kicks in. The easiest way, if there is a boson in the final state, is to just shine a coherent superposition of the boson in question at the right energy. This oscillating classical field will lead to a transition preferentially in the same mode as the bosons in the field.
This is done routinely in lasers, where the atomic decay rate into the lasing mode is enhanced, so that the atom emits the photon into the laser. Similar phenomena can happen in any decay.
Similarly for a fermion, you can suppress the decay by just filling all the modes.
