I hate drenching with dimethox too - they like to spit it out and they hate it, and learn really quick when you're coming to do the 'mean stuff' and can be hard to catch.

But unfortunately, you will have to give them something aside from grain when young, because they simply will not eat enough at this age for medicated grain to be effective.
When I dam raised, I used toltrazuril which is one time in 5 days and doesn't taste bad. Toltrazuril is NOT approved for use in ANY animals in the US and is illegal. Horse Pre Race (where you can buy toltrazuril) is under investigation by FDA, and some people have success and some do not. As a compounding facility, the drug amounts are not that accurate which may be the reason for some people having success and others not. We are switching back to dimethox.
Personally if dam raising, I would consider using rumensin in the adults to reduce the number of cocci shed by the adults into the environment (not approved for dairy goats, but is approved for dairy cattle - approved for meat stock). I would still do coccidia prevention with oral doses for the first few treatments until the kids are eating 1-1.5lbs per kid per day of a medicated feed. ALWAYS do fecals to make sure it's working (midamericaagresearch.net does them for 5.00)
The basis for all of their diets should always be hay/forage. If putting them up, I'd be sure to put them up with hay. I'd probably use this time to feed them their daily ration of grain, too. Here we creep feed medicated grain until about 3-4 months, then ration it to 1-1.5lbs/kid/day. Because slug feeding is less ideal for them, if you can make the kid area a creep feeder during the day that you can lock them in at the evening, that may be more ideal for their gut health IMO.