cow, bull, ox
牯 centers on bovine animals, specifically a cow, bull, or ox. The meanings are closely related, all referring to cattle.
牯 combines 牜 (cow) with 古, which likely provides the sound. It is a phono-semantic compound where the cow radical indicates the meaning and 古 hints at the pronunciation.
The left side 牜 is a cow, and the right side 古 looks like an old story. Imagine an old cow telling ancient tales: 牯 is a cow or bull.
For コ, picture a cow telling an old story to a child named Ko: Ko -> コ, and the cow (牯) is the storyteller.