There's a few possible matches for births of the children, but the best seems to be this one for Patrick :
Name: Patrick Waters
Registration district: Ardee
Event type: Birth
Quarter and year: Jul-Sep 1878
Volume : 2 / Page : 369
A birth cert would show details such as father's occupation, parents full names and allow you to confirm if this is correct. Ardee is the registration district which includes Collon.
There's a birth for this name and year in the extracted collection on familysearch, but without a location or reference numbers - so not possible to confirm if it's the same Patrick Waters.
Name: Patrick Waters
Birth date: 11 Jun 1878
birthplace: Ireland
Parents : James Waters & Anne Graves
There is a possible marriage cross match for this couple in the Ardee Registration district in 1869 - except the year is far to early for Annie, as she would have been 9 at the time. Maybe the way to proceed is with a birth cert for Patrick or one of the other children to confirm Annie maiden name and then search for the marriage.
see these links for notes on searching Irish records, details included on certs, and how to order them from the GRO :
Introduction to Irish Records Ordering Certs from GRO Roscommon Details included on a Marriage Cert Details included on a Birth CertShane