Anne Kennedy was born in 1760 in Croagh, Limerick, Ireland.

BK:

It will be very diffcult to track someone born in 1760. Did your Anne marry and did she stay in Ireland?

Not sure how your Anne would connect to Kennedy families 90 years later but there were three Kennedy families in Croagh civil parish in the 1850 Griffiths Valuation head of household listing.

https://www.failteromhat.com/griffiths/limerick/croagh.htm

There were two Kennedy families in the 1901 census in Croagh civil parish.

http://www.census.nationalarchives.ie/pages/1901/Limerick/Croagh/Clogh_…

http://www.census.nationalarchives.ie/pages/1901/Limerick/Croagh/Clogh_…

Roger McDonnell