I don't know about what is required for a mail contract, but if its required then I guess the ships would have to meet those criteria.
If you have not had the opportunity to look it up by now, the bar is set pretty low.
Any merchant that enjoys a subsidy may also be awarded a Mail contract; this contract is
usually, but not necessarily part of an assigned route.
To qualify to hold the contract, the merchant must set aside (for the duration of the contract) a dedicated 5 dtons of cargo capacity to carry the Mail -- this capacity may not be used for freight, speculative cargo, vehicle stowage, magazine space, or any purpose other than Mail.
The ship must be armed. Presumably this means with more than just sandcasters. (It also goes a long way towards justifying the ubiquity of armed private spacecraft in most TUs.)
A Gunner must be part of the crew roster. No double-duty; it should be a full-time position.
But that's it; ships that qualify and are awarded the contract get KCr25 per Jump in guaranteed income for the duration of the contract (regardless of the actual percentage of the reserved volume that gets used on any particular trip).
It should be a simple matter for governments to also award Mail contracts to non-subsidized, non-scheduled vessels with stipulations that the contract only pays on trips to/from the issuing world, requires some set minimum number of local visits per year, et cetera... IMTU, fee-based "Mail Societies" have formed as sort of a guild clearinghouse to vet (and as necessary, bond) independent vessels holding various regular and irregular Mail contracts.
In setting Mail rates, I charge business and the public a modest Cr1 per parsec fee to send something the size of a DVD through the Mail. The Postmasters see most of this revenue, of course, not the carriers...