Crovect will kill ticks, but you can only buy it in large bottles - if you have a farming neighbour he may be able to give you the amount you need. I think it would be a dose similar to lambs?
I think Spot-on is doing it too, but again it is expensive and quite a large bottle.
You would be best to talk to your vet and get something equivalent to a dog of similar size? As there are no veterinary medicines really licensed for goats your vet can prescribe medicines licensed for other animals under the cascade system - but it has to go through the vets.