A lot of views without comment... so I'll take a stab at it
1. A good vaccination program for your herd will build the immunity of your herd as well as the calves. You should check with your local vet, neighbors, etc. for recommendations. Additionally, vaccinations could (I say could not will) allow you to get paid more for your calves depending upon how you market them. Your vet can work with you on the type of vaccine (killed virus versus modified live that you can give to work with your breeding program)
2. In the opinion of our vet, vaccinations for calves do not begin until they are at least 4 months of age because this is when they have/are developing their own immune system seperate from the cow. As such we do our initial vaccinations at 6 months of age, with their booster shots given at weaning 4 weeks later. Any animals retained within the herd then receive yearly boosters. That being said -- we do some initial calfhood shots within the first 24 hours of birth to give some added protection which is simply Bo-Se (we're in a selenium deficient area), TSV-2 intranasal to assist in prevention of calfhood pneumonia, iodine (actually now Betadine) the umbilical cord as prevention to navel ill, weigh the calf, and apply the ear tag for ease of sorting... multiple bulls and purebred registered herd so we need to know which cow goes with which calf when we seperate them into the breeding pastures.
So with what you've described I do have some questions....
- do you calve in the same pasture every year?
- at the 2 month to 4 month age is there a condition that occurs consistently? dirt lot? windy? that's when you move them into a different pasture?
- how do you treat this cough?
- does it come with a temperature?
- any other symptoms that come along with it? droopy ears? drainage of any sort? lethargic?