Hi, I'm Dr. Bonk. I'm sorry to hear about your calf's troubles. Rectal prolapses are fairly common with diarrhea and straining. The first thing to do is to try to stop the diarrhea. If he is acting normal, eating well, and has no fever, you can give him 2 oz of Kao-Pectate ever 3-4 hours. You can mix this with a little milk or electrolyte solution and feed it through his bottle. You should substitute half of his milk with electrolyte solution as sometimes the richness of the milk causes the diarrhea.
Make sure he is staying hydrated. It doesn't take long for a little guy with diarrhea to dehydrate. You can check this by touching his gums. They should be slimy, not sticky or dry. If he's dehydrated, give him electrolytes without milk or if severe enough, take him to a vet for fluids.
To put the prolapse back, clean it and the area with warm water. If needed, apply some lubricant around the anus and gently push it back in. If he continues to strain and it comes right back out, you'll have to wait until you get the straining under control or see a vet to get it sutured in.
If you can't get it to stay in, keep him somewhere clean and dry. Keep the prolapse moist. You can use mineral oil or vaseline as a protectant. Protect it from direct sun and flies as much as possible. If it is starting to dry out, he needs to see a vet to have it sutured in place.
If the diarrhea and straining are no better with the Kao-pectate within 48 hours, he may need antibiotics from a vet.
I hope this helps. Please contact me with any further questions you may have. Thank you and good luck!