I am not a psychiatrist or medical doctor, but I have had to be aware of medications and there possible effects and uses. I don't know any medications that increase the production of Serotonin. I am not sure that would be advisable. As I recall from my reading, there is a cycle of absorption and release of Serotonin, as well as other neurotransmitters. The neurotransmitters are made from amino acids, which from food and are processed through the body's organs.
Most problems with medication are that the body adjusts to the use of the medication. Prolonged use of SSRIs results in neurons developing more receptors, thus requiring more medication to cover them.
It is interesting that psychotherapy can produce better neurological changes than medication, but it takes more time and perseverance. Learning strategies to overcome the effects of biology has been shown to produce similar and longer-term results than medication, with much fewer side effects. The research shows that a combination of medication and psychotherapy is the most effective (although I think they mean the quickest method for getting long-term effects) because the medication makes accepting the strategies easier and increases compliance. Eventually the medication can be weaned down.