A birth cert should show full names of both parents, along with place and date of birth, father's occupation etc. see notes below on how to order research certs. Since Josie/Josephine is a relatively uncommon name, this is worth investigating, if only to eliminate. Although if she did in fact end up using a different surname it seems possible that she might have altered the first name she used also... a definite connection for her is not going to be easy to prove. Did the address on that marriage appear on any of the children's birth certs ?
Variations in names and place name are quite common, but that said I've never come across the surname Boyleson before, and there's nothing promising under that surname. A search of Irish births registered between 1890 and 1910 shows no exact match for the surname with that spelling, and the closest being two or three registered as Boilson.
The town of Nenagh is located just under 40km (~24 miles) north west of Thurles, but bear in mind that the references on the BMD Index are the names of districts, so the birth I mentioned could have taken place in another part of the district, and not nessecarily in the town.
Following up on the details you mentioned for that 'O'Brien/Boyle marriage, and in particular the father's name, allowing for more variation in Josie's name, and assuming the Thurles story is correct, then there's another possible line of investigation to follow.. A Boyle family in Thurles town on the 1901 census, father Martin a labourer, mother Catherine and several children - one of the children is a 'Johanna' and close to the age reported for your 'Josie' on her death cert. see here I didn't find this family on the Irish 1911 census which could point to them emigrating... it's another line to follow if that Josephine Boyle born Nenagh is eliminated.
To order GRO research certs - download the order form from this link (MSWord document, Dept.of Social Protection or Welfare),
Print out a copy and enter your details in section 1, and your credit card details in section 3. Put the index references for the record you wish to order (name, record type, reg. district, record type, year/quarter, page & volume) in section 2. If you have several certs to order, you can print the references for these on a separate page and attach to the order form.
Ignore the irrelevant sections on the form such as exact date of birth etc, PPS number etc, the forms are more geared to modern official certs for legal purposes. In section 3 tick the 'photocopy' option to select the cheaper research certs. Post (or fax) the completed form to the GRO, the head office address is at the top of the form. Research cert cost € 4 if you include the references above, and no search is required.
Certs are normally delivered by post, but you can opt for delivery by email by ticking the option in section 1 and including an email address.
