This all seems to be going a bit off topic, but if you're interested in Irish English children's chasing rhymes there's 'Moon Penny' compiled by Bill Meek, 'All in All In' (All in All in ! The game is broke up - chanted at the end of a game) compiled by Eilís Brady and 'Boys and Girls Come Out to Play' compiled by Maurice Leyden. In 'Moon Penny' which consists of playing rhymes collected in Dublin, there are two songs that have a chorus in Irish - influenced by children who came to live in the city from elsewhere, I imagine. Though I did see somewhere on this forum or the other one, that there was at one time, a part of Dublin where Irish spoken as a first language.

An Madairín Rua, Rua, Rua, Rua, Rua,
An Madairín tá granna,
An Madairín Rua 'Na lui'sa luachair
'S barr a dha chluis in áirde.

agus
The Shepherd's Lamb

Is Ó goirim goirim thú,
Is grá mo chroí gan cheilig thú,
Is Ó goirim goirim thú,
'S tú peata beag do mháthar.

In the chapter on chasing in 'All in ! All in!', there's Tip and Tig, Sticky Apple, Duck Chasing, I've no Iron, Follow the Arrow, Kick the Can, Relieve-ee-o, Hide and Go Seek, Witches, Catching the Rope, Colour Chasing, Mr. Fox, plus Old Granny Grey and Old Daddy Aiken - rhymes to incite a chaser to try and catch you. What would be their equivalents in Irish?
For your information -
In Irish and in English there's the booklet and DVD 'Spraoi le Chéile - Playing together', the DVD Cluichí Clóis and the file Spreag an Ghaeilge le Spraoi - Scaoil Uait Í (which is available on line) all of which were very kindly sent to me.

At the National Museum (Country Life) at Turlough Park, Co.Mayo - Ard-Mhúsaem na hÉireann, Músaem at tSaoil Faoin Tuath, Pairc Thurlaigh, Caisleán an Bharraigh, Co.Mhaigh Eo, for school visits they have available on loan : Bosca Cluichí Traidisiúnta. In the English version this includes the instructions for Hopscotch, Skipping, Bread and Water, Rings, Donkey, Card Game '25', Skittles, Red Rover, Beds, Chestnuts, Towns and Counties, Statues, FiveSlates, Mowl, Taw the Hole, Woolworths, Sticky Apple, Queenie-I-O, Traffic Lights, Tip Tag, Jackstones and Snap the Bacon. Unfortunately they don't provide the list for these in the Irish version, but anyway aren't these typically Irish-English games rather than what Irish-speaking children would play in the Gaeltacht?