Hi Michele . . .
Welcome to Ireland Reaching Out . . . and to North Tipperary . . .
Glad to try . . . to add to your search . . . .
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First . . I went to Google Maps . . . I entered your Gaelic placename . . (see below)
It chose " BALLINGARRY " . . in NORTH Tipperary . . .
But . . . you have to be aware . . . there are three Ballingarries in Ireland . . . two in Tipp. . . one North . . . and one South
the remainding one is in Limerick . . .
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BIRTH . . . . Martin . . . William . . . Tipp. and all Ireland 1815 +/- 10 yrs .
So . . when I search . . . I rely on " Roots " . . a very reliable (Paid) search engine . . .
I search MARTIN . . . b. 1815 +/- 10yrs. . . .Tipperary . . . Nothing . . . then ALL Ireland . . . Nothing . . . same hor William
Next I try . . . Ancestry . . with NO further joy . . .
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Next I turned to . . . http://titheapplotmentbooks.nationalarchives.ie/search/tab/results.jsp?surname=Vaughan&firstname=&county=Tipperary&townland=&parish=&search=Search&sort=&pageSize=&pager.offset=0
This is a TAX roll . . . from 1823 - 1837 . . . all Ireland . . . Property / Landowners . . .
( see map below . . . Ballingarry SOUTH Tipperary ) . . .
if you look at page 4 . . of the above . . .the very last entry . . is for Mullinahone . . .
this caught my eye . . because it is adjacent . . . to Ballingarry SOUTH Tipp.
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then Limerick . . .
http://titheapplotmentbooks.nationalarchives.ie/search/tab/results.jsp?surname=Vaughan&firstname=&county=Limerick&townland=&parish=&search=Search&sort=&pageSize=&pager.offset=0
NO joy there
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Next to . . . Griffiths Vaaluations ( 1847 - 1864) . . . another TAX roll ( great people for collecting taxes . . back then . . has anything changed ?) . . NO Joy . .
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Next . . . something promising . . .
In the 1901 National Census . . . for Vaughan . . . Tipperary . . . see
http://www.census.nationalarchives.ie/search/results.jsp?searchMoreVisible=false&census_year=1901&surname=Vaughan&firstname=&county19011911=Tipperary&county1821=&county1831=&county1841=&county1851=&barony=&parish=&ward=&townland=&houseNumber=&familyId=&ded=&age=&sex=&search=Search&ageInMonths=&relationToHead=&religion=&education=&occupation=&marriageStatus=&yearsMarried=&birthplace=&nativeCountry=&language=&deafdumb=&causeOfDeath=&yearOfDeath=&familiesNumber=&malesNumber=&femalesNumber=&maleServNumber=&femaleServNumber=&estChurchNumber=&romanCatNumber=&presbNumber=&protNumber=&marriageYears=&childrenBorn=&childrenLiving=
here you see a number of VAUGHAN families (1901) . . . listed for BALLINGARRY . . . NORTH Tipp.
But . . then again . . . when I search further . . . I find a lot of Vaughans . . . living (1901) in Mullinahone SOUTH Tipp . . . near Ballingarry S.Tipp
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So . . . are you thoroughly confused by now ??
Conclusion . . . Your Vaughans . . . I'm guessing . . . most likely . . . came from either Ballingarry N.Tipp . . . or . . . Mullinahone S.Tipp . . .
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Should you wish to go further . . . and spend money . .. theree is a professional sevice available ( not cheap) . . . ( as follows)
https://www.tipperarycoco.ie/heritage/genealogy-centre
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https://registers.nli.ie/parishes/0760
https://registers.nli.ie/parishes/0241
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Best of good luck with your continued search . . .
Best I could do . . . Cheers . . . Eamonn .