Stainless Steel is durable, corrosion resistant, and can be washed or sanitized easily.
I haven't built one of these yet but from my days working at McDonalds at age 15, or as a kid in camp, I recall the standard hot water baths with stainless containers suspended above them covered by a stainless lid. Well, this trough is the same 
p
rinciple but a little more simplistic.
1) Stainless containers are EASY to find,
google. . .
RESTAURANT EQUIPMENT [ Your City Name ]
2) After finding a local dealer, used or new, go there. Purchase one or more trays that you feel will work well. They probably should be anywhere from 1-1/4" to 4" deep, about 6-inches wide, and as long as you can find. These are fairly standard sized utilities in the restaurant business.
The exact depth and width you choose isn't that important so long as the sheep can stick their muzzle in it (if you do, you're watching the food network to much). Prices vary significantly so I'd suggest a web-search before you go to the store so you'll have some idea of what you're buying. Typically speaking, the higher grade of stainless is more expensive since it has more nickel in it. This gives it strength and resistance to rusting (Corrosion). I've seen prices on line from $6.00 - $25.00 for the exact same item - no joke, and if you go to a used store you should be seeing these for at least 30% less.
3) While you're at the store for the trays, measure the opening of the steamer tables used to hold them (Width and length). If not, you'll need to measure the upper most dimension of the pan (Not the lip, but under the lip). This is the inside dimension of the frame you'll need to build - so on the way home, stop and get a few treated 2x4's.
4) Decide how you're going to mount the trays. You'll be building a 2x4 constructed frame to set the pans into. Since it's wood, they can screw into posts (Like the wood trough does) or you can build legs and make it free standing and portable. Portable is nice if you're feeding them inside while a fixed trough can have its own shelter outside the barn. I see it as personal preference but you'll need to add some additional support for the sides (like a piece of plywood) so that the 2x4's don't twist or rock, and, you'll also need to do something along those lines for the overall width.

Also, if you decide on wide trays then I would also add a triangle piece of plywood (like a pyramid) to the sides and screw it the frame, the plywood in turn is screwed to the posts. This will give you the added support to hold the weight of a freaky ewe or ram that jumps onto it. Just don't forget to figure in the width added by the plywood, you'll need to shorted the width of your trough by twice its thickness (I'd use 1/2-inch or better plywood).