Hi Bathonian,
I did a couple of quick checks at
http://www.freebmd.org.uk for any likely matches to the information you've given. I've given the GRO references for promising results - you'll need to filter them against anything else you know but didn't mention.
A word of warning - don't take my word for any of this, double-check everything yourself!
Possible John Griffiths/Ann Morgan marriages 1883-1885 anywhere in Carmarthenshire:I only found two possibilities, both in the Jan-Feb-Mar 1884 quarter. Neither is a perfect match, but both are so close I think that it has to be one or other of them:
1) Llanelly, Volume 11a, Page 933 - John Griffiths + Ann Morgan
s (with an S)
2) Llanelly, Volume 11a, Page 924 - John Griffiths +
Sarah Ann Morgan
I'd start by taking pot luck and ordering one of these. If it's the right one it'll give you the names of John's father and Ann's father. If it's wrong, try the other one!
Possible Ann Morgan births 1862-1864 in Llanelly:Since the marriage search threw up the surname "Morgans" (with an S) and the given name "Sarah Ann", I extended my search to cover these. I searched between 1862 and 1864.
Sep 1862 MORGANS Ann, Llanelly, Volume 11a, Page 5__ [unreadable]
Mar 1863 MORGAN Annie Elizabeth, Llanelly, Volume 11a, Page 562
Mar 1864 MORGAN Sarah Ann, Llanelly, Volume 11a, Page 601
Jun 1864 MORGAN Ann, Llanelly, Volume 11a, Page 653
Jun 1864 MORGAN Sarah Ann, Llanelly, Volume 11a, Page 634
Dec 1864 MORGANS Ann, Llanelly, Volume 11a, Page 562
Nothing here would give a better lead than the marriage certificate. And since both "Ann Morgans" and "Sarah Ann Morgan" have matches, either marriage certificate could be right.
Possible John Griffiths deaths 1888-1890Llangennech was in the Llanelly registration district (see
http://www.ukbmd.org.uk/genuki/reg/districts/llanelly.html ), and a death in a mining accident would be registered there. Only three matching deaths show up for 1888-1890, and two are far too old:
Mar 1889 Griffiths John, Age 61, Llanelly, Volume 11a, Page 546
Sep 1889 Griffiths John, Age 31, Llanelly, Volume 11a, Page 461Mar 1890 Griffiths John, Age 57, Llanelly, Volume 11a, Page 695
The only close match (in bold) would give an 1858 birth year.
Possible John Griffiths births:Too many matches to be useful at this stage. Also note that he may be older than you think (born c1858 not c1861 if the death record above matches).
I hope this gives you some useful leads,
Pete