Many cases of calf diarrhea (especially beef animals) are due to rotavirus, cryptosporidium, coronavirus and enterotoxigenic E coli. Once these animals get weak they will go down and are unable to get up. Some of this weakness is due to poor circulation by the heart and can account for what you are seeing.
The first thing you could do would be to get a fecal check done of the sick calves and a few of those not showing symptoms. Cryptosporidium is a type of coccidia.
Treat the sick ones with electrolyte supplements (many calf scour treatments available) and some type of sulfa antibiotic or penicillin. Tylan or sulfa tribrissen. Replacing the lost fluids and electrolytes is the most important thing you can do. If this is a virus then it has to run its course. Antibiotics will help prevent secondary bacterial infections but will not stop the virus. The virus will kill because the calf dehydrates and looses too many electrolytes.
You could also start giving your calves E coli antiserum when they are given the colostrum.
There are some vaccinations that can be given to the cows before calving and some that can be given orally to the calves as soon as they are born. These vaccines have a questionable effectiveness. Good sanitation can be more effective against coronavirus and rotovirus then some of the vaccines.
If you do not have a source of these type of medications you can look at some of the bigger online catalog companies such as jeffereslivestock.com
If I can answer anything else please let me know.