Hello Patricia,
You could log on to irishfamilyhistoryfoundation website. It's free to subscribe to and you can trawl through many records. You are only charged for the records you want to open. It's not expensive to use. This website contains most birth, marriage and death records going back many years.
I put in your family name Thomas Carey 1830. This gave me 46 birth records in Ireland and when I refined the search to the South Tipperary genealogy centre, it gives a Thomas Carey 1825-1835 in three parishes. You can scroll down through all the parishes and locate where they are. It is only then you are charged if you want to view the actual record.
The parishes were Ardfinnan, Cahir and Powerstown, so one of these may be your ancestor.
Please bear in mind that Tipperary is divided into North Tipperary and South Tipperary Ridings. That means that there are two genealogy centres to look at. I haven't looked yet at North Tipperary. When you go to the map of Ireland you just click on the county and that will take you to your genealogy centre.
I hope you find your ancestors. The detective work is such fun and you'll get such a kick when you find your Thomas Carey.
If I can be of any more assistance to you, please just let me know.
All the best in your quest!!
Kind regards,
Anne Dennehy