I've seem dolmades preserved by pickling, brining and packing in oil. All three methods would require "pressure canning" for safe home canning since they contain meat (lamb). However, when "canned" via one of these methods they usually use "short" grained rice instead of the traditional long grain rice due to the lower starch content.
I'm with Loprraine - I think freezing would be a better option than canning ... certainly cheaper and easier. They could be assembled and frozen uncooked, to be cooked later, or fully cooked and thawed later for serving at room temp or heated in the microwave, or steamed, for serving warm/hot.
When I make dolmades they generally don't last long enough to worry about long term preservation ... if they are not gone the first night they are gone the second day.
"It ain't what you don't know that gets you in trouble. It's what you know for sure that just ain't so." - Mark Twain