Hi Carol,
do you know where Parke is in Mayo - or the area the family came from? Sorry if you have been here already
I looked at Irish Townlands
http://www.thecore.com/seanruad/ - there are lots of places with 'park' in it but there are 2 Park townlands - Turlough Civil Parish and Kilbeagh Civil parish.
Then I looked at Griffiths Valuation (around 1850s so a bit early for your dates)
http://www.failteromhat.com/ for the two places. There are lots of McHales and Roches in Park, Turlough but none in Park, Kilbeagh.
1901 census
http://www.leitrim-roscommon.com/has a Roache entry for Park, Turlough - Edward 74 yrs with a son Thomas 24 yrs and daughter Sarah 20 yrs but no McHales. There are other Roche and McHale families in Turlough civil parish.
Then- should have gone here first really- I went to
http://www.rootsweb.ancestry.com/~irlmayo/records.htmwhere there are some records from Parke Church, Turlough for the relevant years but not yours that I can see
However at least I now know where Parke is and if you didn't - you do too
I've been to the Museum of Country Life in Turlough Park so wonder if that is where it is?
http://www.geocities.com/heartland/acres/4031/RCPARISH.HTML shows that the records are on film and so you should be able to order them from a Local LDS centre.
Broken Linkhope this helps and is of some use to you
heywood