Neurotransmitter control via biofeedback? According to this thread, certain regions of the brain, and even some distributed activation patterns can be up/down regulated via bio-feedback.

Is it possible in theory and is there any research where subjects were taught to consciously control neurotransmitter (e.g. serotonin, dopamine, etc...) levels?

It seems that doing so would present with alternatives to pharmacological methods of altering neurotransmitter levels in treatment of various mood and cognitive disorders.
Firstly, you wouldn't be directly controlling neurotransmitter.  From the human perspective, you'd be controlling higher-level events (and they aren't necessarily describable on more than a phenomenological level).  Of course, this would also lead to some changes in neurotransmitter release, but in a complex way: that's all handled at a lower level by the cells.

That being said, neurofeedback is a (the?) clinical practice that most closely matches your question.  If you look at the references in the wiki page I linked, you will see lots of papers reporting on the findings and techniques.  I do not know the current state of the research.