A cup of coffee has zero carbohydrates, trace lipids, and about half a gram of protein. That's not going to pull anyone out of a fasting state.
Now, if you're talking about a cup of flavoured milk, that's a different question...
People tend to add single or double cream (1/2 & 1/2 or whipping / heavy cream, respectively, in the US) to coffee, both of which have less carbohydrate, and generally add a tablespoon or two (15--30 ml) per cup of coffee. The carbohydrate content is < 2g.
That's unlikely to bring someone out of a ketosis state, which requires a daily intake of < 15--30g. That's about two full cups (450 ml) of single cream.