The ones I've seen premade are fiberglass. You might try exterior grades of wood, but you would want to seal and paint thoroughly. YOu could then use tile or faux-brick as a covering.

I have seen those fiberglass ones too but I was hoping to avoid that kind of expense since this cabinet will be protected from constant direct exposure to the elements. Tile is a pretty good idea. I wonder if I could build a frame out of treated lumber and then cover it with cement board and tile. That might work but I am not sure how I'd do the doors. Something to think about anyway.

Cement board and tile would be fine. You could use external plywood and tile for the doors, or several coats of very good exterior (or marine) paint. Note that if you use a drop-in grill you will need separation from combustable (wood) surfaces. Most of the high-end grills I've seen can be had with a stainless mounting insert that takes care of this.

Make sure you calculate the weight of this cabinet run before you build it. Decks are usually engineered to hold ~55 psf. You don't want to end up making your deck sag.

How about stainless from a restaurant supply place? They also turn up used on Craigslist and supply houses that specialized in used equipment.
I've attached one long list, which might narrow a search for cheaper sources.

Here is a link that might be useful: worktable cabinets