In the sticks they frequently outsource to authorized personally owned vehicles. Those are common all throughout Appalachia for example. They call them rural carrier associates. Here is the pitch:
"As a Postal Service™ Rural Carrier Associate (RCA), you will have a continuous, part-time job with a reliable employer. If you are retired, self-employed, an at-home parent, an educator, night student, or are employed on an evening shift schedule, this on-call position could be the ideal job for you.RCAs are responsible for the safe and efficient delivery and collection of the U.S. Mail™, working part time when regular carriers have scheduled days off or take vacation days. RCAs also sell stamps, supplies, and money orders. RCAs perform a vital function in the Postal Service, serving thousands of families and businesses in rural and suburban areas while traveling millions of miles daily. The work can be demanding—but also rewarding."
And a note about the vehicles:
"Generally, RCAs are required to use their own vehicles for mail delivery, and they receive an equipment allowance in addition to regular pay. The vehicle needs to be insured, dependable, and in good working condition. Vehicles with bucket seats or standard transmission are not recommended. Some offices may provide a Postal Service vehicle."