I believe it's Depot Post Office, as in depot at a railway station. Also referred to as Distributing Post Offices.
According to C.L. Towle, in his book 'U.S. Route and Station Agent Postmarks' Distributing Post Offices were instituted in 1810. Local post masters were able to supplement their incomes through these Distributing Offices, and in h 1850s many of them made more per year than the Postmaster General.