The birth is before the start of statutory registration and so you would probably need to search church records for further early information. Drumclift RC records start in 1841. You can see where copies are held using this link:
http://www.irishtimes.com/ancestor/browse/counties/rcmaps/clarerc.htm
I suspect Margaret?s maiden name may have been Ringrose rather than Ringross. Ringrose is fairly common in Clare.
There?s no sign of Patrick & Margaret in the 1901 Irish census so they must both have died before that. I searched for a death of Patrick Henchy in Co Clare 1864 (when records start) to 1901. The only one was someone whose death was registered in Corofin Jul ? Sep 1887, volume 4 page 106. Est year of birth 1808.
Corofin is in a different parish to Drumclift and I have no way of saying whether it?s your family but perhaps the death cert might give a clue. His marital status or the informant (?Margaret perhaps) might reveal more.
Searching for Margaret?s death revealed only 1 possible match. Registered Ennis (which is the civil registration town for Drumcliff/Drumclift) Jan ? Mar 1895 Vol 4, page 145. The estimated year of birth was 1840 which appears to makes it tight for her to be the mother of Michael b 1856 but the age is just the informant?s best guess and is often out by a factor of up to 10 years.
You can order a photocopy of these certs from GRO Roscommon for ?4. Put the place, year, quarter (if there is one), volume & page number on the application form (anywhere). http://www.groireland.ie/ You have to post or fax the form to them but they will e-mail the copy certificate to you if you wish. Put ?please e-mail to?..? clearly on the top of the form.