Cable
The cable you're looking for is Type UF, or Underground Feeder cable.
It can be purchased at big orange, and big blue, by the foot. It's available in 6/2, 6/2 with ground, 6/3, and 6/3 with ground, and is rated for direct burial.
Attachment to Service
There is one temporary, and two permanent ways to supply power to a park trailer.
Temporary
Power-Supply Cord
You'll want to use a NEMA 14-50 receptacle, and 4 wire cord with NEMA 14-50 plug to connect the trailer to the service. The trailer's electrical grounding will be through the service plug, so only the distribution panel will have to be grounded.
Permanent
Mast Weatherhead
You can use four continuously insulated, color-coded feeder conductors strung from a mast to a weatherhead as a permanent feeder.
Raceway
A metal raceway, rigid nonmetallic conduit, or liquidtight flexible nonmetallic conduit, from the disconnecting means to a junction box on the underside of the trailer can serve as a pathway to run permanently attached feeders.
NEC
For reference, park trailers are covered in article 552 of the National Electrical Code.
A 30A connection will require a much heavier wiring connection than either 12 AWG or 14 AWG. It is common that a 40A or 50A cord is used to hook up a range unit. These can be purchased in several lengths with molded on plugs at the end.
As always make sure that your outlet, wiring back to the entrance panel and the circuit breakers are sized properly for the load. The circuit components are normally rated a bit higher than the maximum current draw of the range. So a range unit that pulls 30 or 32A should be on a 40A circuit.
Best Answer
This is not exactly a good idea because how will the next home owner know that you installed a 10AMP socket with a 15AMP breaker. Your sockets should definitely be at LEAST at the level of your breaker otherwise the following could happen.
Someone comes in and changes the oven one day and checks the breaker box to see how many amps you can use. They see a 15A breaker and say great I can put a 12A load on this no problem. Then you are sucking 12A from a 10A socket. This will be fine for short spurts but if someone wants to do something like say, the oven auto cleaning cycle, then that socket could melt and start a fire without ever tripping the breaker.
Sockets MUST be rated as high or higher than the breaker that is supplying them.