[MRM]

A small general contractor would do it, but is probably too busy this late into the construction season.

The trade you are looking for is a framing contractor or rough carpenter. Anyone who does framing will be able to do a deck for you. A finish carpenter probably could but will charge too much, take too long and will make everything too perfect. Search the Internet in the area for a reputable company that holds itself out as a framing subcontractor to residential general contractors. That's who does decks when they're new.