If you have not yet built your wall, and are flexible in how you build it, fitting between the studs can work.
These foam panels come as 4' x 8' sheets, and for some strange reason, many come pre-scored at 16 (3 panels per sheet) and/or 24" (two panels per sheet). That sounds good until you realize that walls are often framed 16" on center from 2 x 4 lumber, (16" OC allows all subsequent panels of siding, drywall, etc. to butt on a stud and divides the span so the panel is supported across it's span in 4 places) so that leaves wall cavities of 14 1/2 inches, meaning you have to prune 1 1/2 inches from the side of each panel scored and snapped to be 16", meaning a bunch of labor, and a particularly messy type of expensive scrap left over from the cut. If you go 2' on center, you still end up trying to fit a 24" panel into a wall cavity of 22 1/2 inches.
So what this is telling us is these panels are not really intended to be used inside typical stud walls. They are for sheathing on the outside, under roofs, under cement floors, outside concrete walls, etc. By comparison, standard fiberglass batt insulation comes in a standard width of 15 inches, which is perfect to press into these wall cavities to seal them up. But for our use, glass batts are about the very last thing you would want to use. Rodents, wet insulation, etc. make them truly horrible for this use.
So back to the panels, one way around the odd shaped cavity issue is to not use vertical studs. If the coop is small, you could abandon the vertical wall studs and go horizontal for the main sides. That leaves the 4 corner posts as the structural supports bearing the weight of the roof and horizontal lumber as the support for hanging the siding, which if you use plywood or T1-11 siding is structural itself. Do that and you can easily space these horizontal runners so you can fit a 24" wide panel in. Use 1 1/2 inch thickness so they are flush with the runners, sandwiched between the interior and exterior walls.
Yet another option, is to abandon the 4' x 8' sheets of plywood for exteriors so you don't have to adhere to the 16" or 24" OC stud pattern. You could use horizontal boards (like the traditional ship lap) or perhaps vinyl siding. Or if you use these full sheets on the exterior between the insulation and metal siding, which if installed over insulation makes for a good exterior wall sheathing. Metal siding is maintenance free, durable and predators won't have any success with it.
Whatever the case, don't lose sight of the purpose of the insulation, which is to install a thermal break to prevent the line of sight radiant heat generated by the birds from hitting the uninsulated exterior wall and then pass through that wall to radiate out into the open. You want to trap that radiant heat in the building. Additionally, any insulation will also help to reflect summer sun and heat away from the building. Both take a little but do not require a lot.