@Double R Ranch is right .... I have offered free access to water from the start and have had MOST calves just do fine. A few will drink water til they are sick.... so mostly I watch and see... if some do not want a bottle, the first thing I do is take away the water.
If no signs of "naval ill" like
@MurraysMutts is suggesting, then you go the next step.
Yes... the Quality of the milk replacer is paramount. I also do NOT feed medicated milk replacer... it can suppress but not actually "treat" problems and they become chronic.
The milk replacer HAS TO BE ONLY MILK BASED.... soy can be a death sentence to most calves early on. I also feed the 20/20 which is fat and protein... and it has to be derived from milk/milk whey based.....
Agree, calves should be wanting more when being fed bottles...
The quantity varies with different breeds and such. I do not feed a whole 2 qt bottle to a jersey baby calf at a feeding... too much for the milk stomach to hold and process all at once. Big holstein bull calves can take it. Now it is popular for many dairies to give calves 3 qt bottles at a feeding... maybe after a couple weeks, but to me it is just too much of a GLUT of milk in their stomachs.
Think about kids, they will eat candy or sweet snacks til they are finally full... but then get sick later... Bottle calves are not going to stop drinking until they are full to the brim, but then pay for it later... a calf on a cow gets all it wants FROM DAY 1... they drink til they are full... and go back later and get a little more... A beef cow NORMALLY will only produce and let down 1-2 qts in the beginning so the calf will not get too much in most cases. As they butt that udder, the milk let down is more, and the demand of nursing stimulates the mammary glands to produce more... Their intake increases as the amount produced is increased... but they are getting this increase over 4-6-8 feedings a day at only 1-2 qts at a time that they are accustomed to. The amount of "milkiness" in beef cattle varies, with some lines making much more milk than others... but the general idea is they will produce and let down what the calf can drink and hold at a time and they will go back for more when they get hungry and get a little more then.
You need to get at least a week in before you can be sure that the calf's problems with not wanting to eat are nutritional/coccidia based. If it were my calf... and this is ONLY from your descriptions, I am NOT a vet.... I would feed 1/2 bottle 3 times a day and give the corid for scours.... I would NOT have water in front of him... If he is not playing and wanting to run around some, there are some other things at work and without having any eyes on, I have no other suggestions except a vet visit... I am thinking the calf has something else going on if it doesn't seem to resolve its self. If it is a rota virus or a corona virus, I do not think corid will do it any good. That requires an antibiotic and probably several shots in a series... and both of them are real b#@ches to deal with...
You might want to try taking him off milk completely for 2 days, feeding only electrolyte solution... get his system "emptied out" and then go back to adding milk for 1 or 2 feedings... for the nutrition...
I don't know without seeing him first hand. But I am in total agreement with
@Double R Ranch ..... half the problems with baby calves is the kind of milk replacer and OVERFEEDING in the beginning.