Slate has been despatched by rail from North Wales since the 1950s.
There were (at least!) four sources of slate served by rail in North Wales, and all lasted into the 1960s; they were Blaenau Ffestiniog, Nantlle, Port Dinorwic, and Port Penrhyn. There were no connections between the Penryn Quarry and Bethesda station, nor between the Dinorwic Quarries and Llanberis station, and therefore (as a general rule) no slate would have been moved from those stations. Moreover, neither had the slate transshipment facilities found in Blaenau and Nantlle.
Photos exist showing BR shunts at Port Dinorwic and Port Penrhyn in 1961. The last train on the Penrhyn Quarry
"main line" between the quarry and the port ran on 27th July 1962, and it's reasonable to assume that the last slate was shipped by BR from the Port at about that time; circuit wagons were provided by BR specially for the transport of Penrhyn Quarry slate (these were marked up with something like "RETURN TO PORT PENRHYN, LMR"), and some could usually be seen from passing trains parked-up on the branch between the North Wales coast main line and Port Penrhyn. As the Padarn Railway (which linked the Llanberis quarries to Port Dinorwic) closed in late 1961, it's reasonable to assume that slate from Port Dinorwic also ceased at about the same time.
From memory and what I've found by a quick
"dig", I'm a bit confused regarding Blaenau Ffestiniog.
I watched the connecting line built between the former LNWR and GWR stations at Blaenau; from memory, the standard gauge line was on the south side of the formation, and the narrow gauge remained on the north side. Moreover, a separate arch was constructed beneath the A496 road solely for use by narrow gauge slate trains accessing the North station yard from the Fotty & Bowydd/Duffws/etc quarries. Wikipedia states that the connection between the two former stations opened in 1964, but that seems a bit late to me; however, if it is correct, for BR to have constructed an overbridge to permit slate from the quarries to enter the yard by narrow gauge railway, there must still have been some slate traffic using the Conwy Valley branch at that time.
I also recall seeing a narrow gauge slate train entering the yard at the north western corner on the link from the Oakley Quarry; I can't be specific on the date, but it must have been in the 1960-1964 period.
According to Wikipedia, Blaenau Ffestiniog North closed to general freight in May 1964, but wagonload continued until 1982; again, I would have thought the 1964 date to be early, as it was usual to pass a local freight (usually hauled by an Ivatt class 2 2-6-2T) on a down-hill service when going up-hill on a morning DMU. There always also seemed to be a BR Thorneycroft lorry parked-up on the platform at North station at that time! Moreover, I've also found a photo of the branch freight at Betws-y-Coed in 1965, and this includes in the formation a shock wagon; these were often used to carry slate.
Finally, Nantlle.
Slate traffic from Nantlle also has the distinction of being the last use of horses on BR; (try this link to the Wikipedia entry for the Nantlle Railway which shows a horse-drawn slate train in 1959, and reference is also made in the entry to a demonstration being given as to how the horses were worked at the Festiniog Railway's Centenary of Steam celebration in 1963:
https://en.wikipedia.org/wiki/Nantlle_Railway); however, the poor horse died right at the end of the railway's life, and it was replaced by a tractor by the time the narrow gauge portion closed in December 1963 and was also used for a railtour in October of the same year - see:
https://c2.staticflickr.com/6/5225/5551042268_18632765f9_b.jpg
This slate traffic was handled in two parts; horses/a tractor pulled the slate on the narrow gauge section of the line between the quarries and Nantlle station, and then it was transshipped to standard gauge wagons for the rest of the branch to Pen-y-Groes, and then via Caernarfon to join the North Wales coast main line at Menai Bridge for onward transit to the ultimate destination. Therefore, it's reasonable to assume that slate from Nantlle continued until late in 1963. Every time I saw the Nantlle branch freight it was hauled by a Stanier '5' with the loco facing towards Nantlle.
Finally, recovery of slate waste from the Blaenau tips for re-use.
Some was removed in about 1980, crushed, and then used to raise the level of the land in Glanypwll, to the west of the A496 Pencefn Road; sorry I can't be more specific about the date, but it was certainly before the Festiniog Railway re-opened back to Blaenau (in 1982) as some of the old trackbed - adjacent to North Western Road - was used to transport the waste between the slate tips being recovered and the land were it was being
"dumped".
Obviously, most of this is from memory, but I have tried to validate what I remember from published sources wherever possible