If these people attended the Armagh RC Parish - records from 1796 baptisms, marriages from 1802 with gaps.
Church of Ireland from 1801.
Other Parish records are a mixture of dates.
A birth record usually give both mother and father's name as well as mother's maiden name, parish/place, date.
The above is from an Irish Heritage Foundation that has members from most of the counties in Ireland. It is a not for profit Foundation but fee based (like most of Ireland)www.emeraldancestors.com
You could try the Tithe records of the 1820-30's for the parents of this couple. They are available on Ancestry.com
with a date, name and place (if different parish from Armagh then I could look up the dates again)
They are also available at PRONI, Belfast and the National Archives, Dublin.
You can use the Griffith Valuation to find Parish's in common for the names Webster and Woods in an effort to find a parish for example:
There are 10 Webster's in 5 Parish's in 1864 Griffith's
There are 155 Wood's in many parish's. The ones they
share with the Websters are:
Armagh 2 Websters/10 Woods (Union Armagh)
Derrynoose 2 Webster/20 Woods (Union Armagh)
Killyman 1 Webster/0 Woods (Union Armagh)
Lisnadill 5 Webster/2 Woods (Union Armagh)
Tartaraghan 1 Webster/19 Woods (Union Armagh)
This means all these parish's are within a 12 mile radius of the town of Armagh and all eligible for your description.
The names of the Webster's are Thomas, James, 2 x Samuel,
3 x John, 2 x William, 1 Dorah. These names should appear in Letitia's children.
You can use www.askaboutireland.ie
to look in those Parish's for the names of the Wood's living there, again his father's name would show in Robert Wood's children.
other resources, each county has difference information:www.censusfinder.com