Here are 3 or 4 possibilities to consider:
A paper target based on the NMLRA 200 yard metallic silhouette target: A standing bear, rough dimensions 13" wide by 35" high
The NMLRA bullseye target for 200 yds, a 12" diameter black 8 ring, 20" diameter 6 ring
The NMLRA 200 yd musket bullseye target: 8 ring(black) of 16", 6 ring of 24" diameter
or, do a search for 200 yard offhand here on the ALR and you'll find some references to a 200 yard challenge where the target was described as: 22" x 28" with 5" White Bullseye, 12" Black Inner, and remaining area White Outer. Look hard enough and you'll likely find a picture of it as well.
Patched roundball at 200 yards isn't as impossible as it sounds, but you have to have a really flexible mental attitude with respect to your sight picture if you're shooting fixed iron sights, and it takes some experimentation and practice to learn what the sight picture needs to be. (Let me caveat that: 25 years ago when I used to shoot BP silhouette it wasn't that impossible; it may be pretty difficult now.) As to number of shots in a relay, I'd probably go with 10 shots in two consecutive relays, or else 5 shots in one relay. If the shooting is to be done standing offhand, I'd make it 10 shots. If "any military position" (i.e. kneeling, sitting, standing provided the gun is only supported by shooter's hands) 5 shots.