Stretchers have been constructed from wood for centuries, so there are many references out there. But the defining qualities of appropriate wood for stretchers is:
- Relatively cheap and abundant
- Relatively knot free and reasonably true
You'll find the most "heavy duty" stretchers you can buy from the fanciest art supply houses are usually made from material like clear pine. Key parts like braces and (especially) corners are often hardwood. But, by and large, most modern stretchers are mostly made of clear pine.
The strength and stability comes more from the construction, not necessarily the material. Though, obviously, clear pine is chosen over construction grade because if it does want to move, it'll probably move as one piece in a consistent manner. Less likely to split through a knot, as well.
But it's the joinery, bracing, and technique of keeping most members under tension that makes the biggest difference to long-term stability.
That being said, the largest installations now call for steel or aluminum stretchers.