In order to Renew a U.S. Passport from Dumaguete you need two things.
1. A courier, Air21 for sending and returning your passport from the Embassy in Manila. P240 is the round trip cost. Contrary to what is posted on Google, they are located at the back of the Octagon Computer Store at the intersection of Perdices/Acacia Pinili Streets and their phone number is 035 422 6349.
If you take your document requirements to the store, they will be organized in the proper order and will put them in a brown envelope. Also their contract with the U.S. Embassy requires them to pickup at your residence the brown envelope with the payment of P240. The new passport will be delivered to your residence.
To check on the progress of your new passport this link will allow that. https://passportstatus.state.gov/Search
The status doesn't take into consideration we are living in the Philippines and it takes a while for the Passport to arrive at the U.S. Embassy in Manila. The two day delivery may only apply to U.S. residents.
2. A Managers Check for U.S. Dollars from a bank approved by the U.S. government.
This is the tricky part. The approved banks require you to have a U.S. Dollar account with them to issue a Managers Check which is drawn on a U.S. International bank which they have an account for such matters. Read closely the instructions on the Embassy website for any alternatives.
https://ph.usembassy.gov/u-s-citizen-services/passports/renew-an-adult-10-year-validity-passport/
I needed to renew my expiring passport before going to Cebu for passport stamping, converting my approved status to 13a for marriage to a filipina. I am waiting for my new passport.