Fan chart dead ends for Irish relatives - recommended resources?

I have my fan chart completely filled in besides some of my Irish Ancestors. Any suggestions for specific resources? I've looked at some free public sources, but haven't gotten very far. I don't know why it's been so much harder to find my Irish branches than other nationalities...

b. 1839 County Mayo, Ireland
b. 1839 County Clare, Ireland
b. 1805 possibly Athlone, County Roscommon, Ireland
b. 1831 Ireland
b. 1808 County Donegal, Ireland
b. 1785 Ireland
b. 1789 Ireland