At a rough guess, the Durham coal would all come to Whitby in NER hoppers, and the Yorkshire stuff mostly in PO wagons, with perhaps some in railway-owned minerals depending on the colliery.
As for the S&W coast line and its coal deliveries, the old 1:2500 maps don't seem to show coal drops as such -- Robin Hoods Bay has a Coal Depôt, sure enough, but the 1910 & 1926 maps show a couple of plain sidings, at a slightly lower level than the running line, with no indication of a structure that might be drops. This is perplexing, as steel hoppers keep showing up in photos of pick-up goods from the 1950s & 60s! So clearly I'm missing something somewhere. :-D Anyone know of any evidence of coal drops anywhere on the line? I know someone mentioned some at RHB further up the thread, so I'd be delighted to be put straight.