certs can be got from roscommon GRO , you can order and pay by credit card by fax .
when searching for edwards birth ask GRO to search for other childrens births using there names dates and parents names as data .
edward cotter marriages youghal 1872 volume 9 page 506
mary walsh marriages (same details)
this will give there addresses there occupations and fathers names .
edward cotter birth youghal (district) oct-dec 1879 volume 4 page 853
will give mam and dads full name there address and dads occupation .
from certs you should be able to work out parish church ,
write to parish church and ask for copys of entrys for parents marriage and births of children (baptismal) these should give added details witnesses and god parents .
a small donation helps , however some churchs will not help or have high fees , searching through church of latter day saints micro films for parish will be your option .
hope this helps