Is there an equivalent to 14/2 UF that is stranded? If so how is it designated?
No there isnt an equivalent thats stranded. What can be done is install non-metallic rigid conduit(electrical pvc) in the ground at the required depth(24" from grade to the top of the conduit meets all requirements) and use THHN instead of a sheathed cable. Both ends of the conduit must be terminated into a box such as a Bell box.
Given that you specified UF, it implies a wet location, and therefore you need THWN. Most wire is rated both THHN and THWN, but it always pays to check.