So as mentioned, I cannot find any reference to "myukin ミュキン" that isn't related to Hyouge Mono, so I believe it's one of Oribe's self-invented terms. But this is the colour of the box in the anime:
Mild spoiler ahead:
This is an actual Oribe ware from Wikipedia; to my knowledge the most well-known kind
We had a couple of Oribe equipment in our university tea club, was my favourite to use. Back then I didn't know it was Oribe-style though
I think ミュキン has something to do with the colours of the box and the symbolism of green as budding/renewal of nature, which leads into the joke of Oribe thinking Osen's "taste" is having sex outside.