No record of anybody named Henry Charles Clark anywhere in Ireland in 1864 - 1868 in the statutory records.
I doubt the presence or absence of the letter ?e? at the end of the surname has anything to do with possible English origins or a concern for the name being too English. In the 1800s people didn?t bother with the spelling of their surname. (Most of them were barely literate anyway, and weren?t going to worry too much about precise spelling). The idea of a single ?correct? version is very much a 20th century preoccupation. If searching the records, keep an open mind on the spelling. Expect it to vary, according to the whim of the person recording the information.
There is just 1 Margaret Connors birth in Mallow in 1871, Vol 15, page 508. You can order a photocopy of the certificate from GRO Roscommon for ?4. http://www.welfare.ie/en/Pages/Apply-for-Certificates.aspx
You have to download and print off the form. Then either post or fax it back to them. You can?t e-mail it to them. However if you want them to e-mail the cert to back to you, they will do that, so tick the relevant box.
Put the reference details on the form (anywhere). Don?t worry about leaving some boxes blank. As long as GRO have the location, name(s), year, quarter (where there is one), volume and page number they should find it.