Hi Maria
I'm a Kelper, and this post rather leapt out at me
The Tripod page is an OLD OLD one of mine - with a dead email address; I'm still around as a person but I haven't progressed a whole lot on that page or updated it in years, actually can't even get in to update it anymore (I was off the internet for a long time)
The Hill cove birth cert will be registered in Stanley and writing to the Registry Office would get you the documentation you want. I think they may charge these days, too.
The other avenue you can try first perhaps is writing to the local "paper' the Penguin News with your Genealogy & Historical Interest Story, and ask for any descendant or helpful people so to either write to your cousin's Dad or to email someone . You may get people willing to nip down to Registers Office, or Graveyard, or even someone in the Camp. I'll ask my Dad too - it's 's surprising what he knows of the old folk after hearing all the stories and names discussed over the years!
Did your cousin's family stop in FI or all leave - I do know of at least one JOHNSON family - but unsure if it's the same. PM me if you want, with any extra info which may be too personal or recent to put on public show
Cheers Chay
AMBLY