Could ingesting the finish on a coffee table harm a 9 1/2-month-old?
Babies at this age often try to chew on anything in sight, in part as a response to teething and also as a way of exploring their environment. You didn't mention what kind of finish is on your coffee table, so I can't say for certain if it would be harmful. But, in any event, repeated chewing of the table eventually will damage the table even if it doesn't harm your daughter.
Try padding the table edges with something soft, such as a rolled towel taped to the table. Or, whenever she goes for the table, offer her something more appropriate to chew on, such as a teething toy or a clean washcloth.
Eventually, she'll get the idea that the table is not for chewing. This will be just one of many items she'll try to ingest. Keep a close eye on hershe's just trying to learn!