Synthesize coumarin from 4-allyl-2-methoxyphenol (eugenol)
Since no-one has offered an answer I'm going to try but as I have no database access some of this is a bit flaky.


Heat (maybe microwave) to give multiple Claisen rearrangement products then separate to isolate 2-allyl, 6-methoxyphenol. This is the flakiest step.
Hydroborate with oxidative work-up to take the allyl to propionic acid.
Ring close (PTSA, Toluene) 
Reflux over activated MnO2 to introduce double bond.
Treat with BBr3 to remove Me from MeO group
Zn reduction of OH to H