Coccidia poop is watery, blackish and often has blood in it in later stages. Sounds like she has a belly ache instead. Her poop will remain yellow and pasty for a week or two, that is normal. You might not see it because her mom will eat it when cleaning her up. The little goat raising don't usually appear for another few weeks when she starts nibbling hay.
Since she has been doing well on the formula for the past week, I don't think the problem is the formula. Her behavior sounds more like the way a baby approaches the bottle when they have gas. Since sheep and goats can't burp, gas can cause bloat.
It you think it is bloat, and know how to tube a sheep or goat, you can try tubing her to release any gas. (This worked at a fair one year when a child overfed grain and her goat started to bloat. Luckily I had a stomach tube in my medical box, and we were able to tube the goat and release the gas and undigested grain which also came up in the tube). If you don't know how to tube a sheep or goat, this won't work.
First, I would cut the formula with 1/3 water to lessen the richness and protein content for a day to see if that helps. Also, cut back on the amount you are feeding in case she is overeating. This could be a problem in a bottle baby if you are giving her all she is willing to eat. Remember that the udder on a constantly nursing doe will empty sooner and the nursing kid will be satisfied with smaller amounts.
Next, you can give her some Pepto Bismol (the pink stuff) to help if she has a stomach issue. Some people give unpasteurized yogurt to help the gut. Or you can give a little bit of paste probiotics (available at the feed store in a tube) which I prefer since it is salty on the tongue and you can follow it with a water bottle. If she continues to refuse to eat, use some electrolyte paste (again available at the feed store) followed by a water bottle to keep her mineral levels up.. Putting Karo syrup on the nipple 0f the water bottle will help encourage her to suck.
How often are you feeding her? How much at a time? Vaccinate asap with CDT.
Hope this clears up.