Do you mean Athlone in Westmeath?
Would be useful to anyone trying to help you to give a clearer idea of dates. For example, if your great-great-grandmother was born sometime after 1864 he birth will probably have been registered and you could send for her birth certificate but if she was born before 1864 there will be no birth certificate and you would need to try to locate church records.
There is a Mary Ann Costello, daughter of Edward Costello & Margaret O'Hay, on IGI. She was born c1860 Ireland and died 12 July 1941 according to IGI but this is a submitted records and should be viewed with extreme caution.
If this is the correct family there are other children besides Mary Ann listed: Hugh c1858 in Ireland and the rest in Liverpool: Patrick 1862, John 1863, Edward 1864, Thomas Robert 1869, Johanes Joseph 1873.