Hi Barbara
Welcome to the IrelandXO Roscommon community!
As Roger suggests, you should definitely add your family details to the ancestor database and ...
I think your starting point should be the parish of KILGLASS which is situated just north-east of Strokestown. (Catholic Parish Records for Kilglass only date back to 1865).
GREEN + MULLIGAN IN KILGLASS
In the years leading up to the Great Famine, the townland of Ballyfeeny was a stronghold for the Green family, which just so happens to be next-door to the Mulligan stronghold of Tully.
By the time of Griffith's Valuation, no Green in the county has land to their name, and only John Mulligan of Carrigeen held on to his land in the parish of Kilglass (albeit a half acre).
County Roscommon hotspots for Mulligan (1858)
https://www.johngrenham.com/ 1850s map Green+Mulligan
Roger is certainly right about them being small farmers; I'd go so far as to say they were cottagers / cottiers, possibly living on a rundale system under the name of someone in their extended family. In this case, they would have most certainly married within the parish, very likely within the same townland (or those adjoining it).
According to Tithe Applotment Records (pre-famine tax-records), Kilglass is the only parish on Co. Roscommon where Greens and Mulligans co-existed.
Green Townlands in KILGLASS parish see: Ballyfeeny(adjascent to Tully); Carrownskeheen; Knockhall; Moyglass
Mulligan Townlands in KILGLASS parish see: Carrigeen; Tully (adjascent to Ballyfeeny)
Ballyfeeny & Tully are the only townlands on this list adjascent to each other, but you could do some map research to determine whether any of the others are in proximity to each other (e.g. one townland apart). What you will discover here in the tithe applotment records, is the names of other parties with whom they shared rundale land, most certainly in-laws. One of those names may have survived the cull to appear on the Griffiths valuation records, and this may give you a position on the map, if not possible kin.
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Mulligan Parishes [Tithe Applotment Records ROSCOMMON]
Athleague; Kilbride, Kilgefin, Kilglass, Roscommon, St Peter's Athlone, Taughboyne, Tibohine.
Green Parishes [Tithe Applotment Records ROSCOMMON]
Ballintober; Cam; Clooncraff; Cloontuskert; Cloonygormican; Elphin; Kilglass; Kilkeevin; Killinvoy, Killukin; Kilmeane; Kiltoom; Kiltullagh; Lissonuffy; St Peter's Athlone; Termonbarry; Tibohine.
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You might also keep an eye on the parish of TIBOHINE, namely the townlands of Mullen and Dungar (Commons of Frenchpark) where a Green and Mulligan lived in proximity.
Hope this helps you find your way home ...
Best of luck,
Rua