Suggestions from someone who has raised more orphans than I want to think about:
1) child gate on the bathroom or a playpen. note: he will grow out of that play pen really fast. Get him in an outside pen as soon as possible.
2) diapers. Yup. Cut a hole out for the tail. Since he's a ram, get huggies or some brand that is padded in front for boys. Make sure you get them big enough to keep "little willie" inside when he stretches to urinate and also not to pressure the hip joints.
3) put pre-ruminant mix out to get him used to solid food. ground corn, ground soybean meal, ground alfalfa, a little sheep mineral.
4) once he gets to the point of finishing a bottle in one feeding, get him on a fenceline feeder. With a bigger bottle hanging on the fence in his outside pen, he can feed himself.
Please, please! for your own safety, remember this is a ram and not a dog. Don't pet the top of his head. Approach him with your palm up and under his chin. Sheep, especially rams, need to keep some respect and fear of humans. This little cutie will grow up and he will probably weigh 300lbs. People forget this and every year some one ends up in the news killed by their sheep.
Yeah, what she said!
I too have raised more orphans thanI can remember. Although a few friends have trained baby goats to a "litter box" goats are smarter. You little guy is just doing what comes natural when it comes to going potty. And because he is a boy, they do it more!
Diapers do work!
If you are not going to wether him (get him castrated at a young age) I agree- be careful how you handle the little guy. He's cute now, but a friend made the mistake trying to make a little ram her pet. He darn near broke her leg from ramming behavior, which is normal for an in-tact male sheep.
When introducing feed, make sure it is safe for sheep. Other kinds are too high in copper.
A ticking clock helps replicate the heartbeat and will comfort him.
You can google some good feeding schedules for bottle babies and introductions of feeds stuff.
Start getting him used to being in a barn/outdoor environment soon, even if it just visits until he is big enough to keep himself warm, and don't treat him like a puppy because he is going to grow fast and start jumping all over the furniture real quick.