It is possible to search for enzymes or a series of enzymes that will take similar reactants to similar products.
ReBIT allows you to query enzymes by your molecular structures of interest using their SMILES code. Unfortunately, a quick search using coumarin didn't produce any results but searches for phenol and phenolate gave some hits.
If you're seeking to do a more extensive search, I would suggest BRENDA. There you can search for reaction substrates and reaction products and even both. Both strategies may provide you with an enzyme that does the transformation chemistry that you're looking for.
Lastly there is always ENZYME, The Enzyme Data Bank. There you can search for chemical compounds. I did a search of coumarin and there are a few hits but they are for methyl-transferases and hydrolases. A more extensive search may give you a few leads.
Most of the concepts that I just suggested are explained in the following review: De novo biosynthetic pathways: rational design of microbial chemical factories.