The majority of kids will not ever have any problems with cocci if your stabling environment is reasonably clean. The ones that have (in my experience the ones that may have been a bit slower on the colostrum take-up) get a dose of vecoxan if and when needed. Sometimes you need to repeat the dose after three weeks.
It is difficult to detect the "bad" coccidia in FEC, especially in older goats, as they can have a high number of non-harmful coccidia in their system. To differentiate between harmful and non-harmful coccidia is expensive and rarely done.
Re worming as said above - unless FEC indicates (and at this time of year it should really only be nematodirus), no need to worm.
Is the kid otherwise fine and bouncy? Temperature? Chest sounds ok?
Also remember that goats can get both viral and bacterial diarrhoea, just like humans... If they are on real milk I would continue with it, and if lots of diarrhoea put some rehydration stuff into the milk (like Rehydion), but not give any concentrate. Just hay. If on milk replacer I would just give bottle of warm water with Rehydion, then start again with diluted bottles and build up to your usual strength over a couple of days. Rea milk does not need to be diluted.
Hope it's nothing serious - have they had their Lambivac/Ovipast yet?