Dear Maria,
Lets look at what you know...
You said Annie Corcoran died in 1882, did she die in Ireland, did you get the death certificate? if not do get it as if it is in Ireland it will give you more information i.e place & informant, were there any more family? maybe some stayed. you an search for family at familysearch.org. In USA there are family search centres where you can order the microfilm based on the information you get on their site( free site) this site is run by the Latter Day Saints & they have a wonderful online collection of information.. Civil registeration started in this country in 1864 so you are well within those dates, so hopefully we should be able to help you. Clarkes are mainly in co Cavan which is next door to co Monaghan & they are plentiful, I have 100's in my family alas I have reached out to some who are related but they are not interested, anyway I plough on....
Best of luck in your saerches & if I can direct you further please let me know. Happy St Patrick's Day. Carmel