A Japanese garden does not have moss - it is of a plain cobble construction with one simple feature plant.

Actually, Bulbaholic, that sounds like a Chinese scholar's garden. Check out vancouverchinesegarden.com.
Some Japanese gardens are done in imitation of that style, while most show a variety of different styles, depending on their vintage, or the taste of the owner. Included in these styles is the moss garden, with an open canopy of deciduous trees, sheltering a carpet of various species of moss--usually painstakingly swept clean by the gardener's apprentice! :)

I don't know if you saw a program with on the BBC about making gardens in small spaces, a couple on there did a Japanese garden and he showed them how to make it using milk and blending it up with one piece of moss. He then painted it on a brick and some stones.. I think it's on BBC Iplayer, might be worth a watch

I get moss growing between my paving slabs. You could ask neighbours if they have any then go and scrape it off for them.

Thanks for the advice everyone, I did see the episode your writing about, I've seen a lot of these videos whether it be blend the moss or grate it but never a '2 months later' video so I'm not sure if it actually works or not.

With all the rain we have had you could easily transfer some off old tree stumps,stones etc keep moist or let it grow near a water source .At the moment it's growing all over the place such as dry stone walls.The Japanese do indeed have a moss obsession Wabi Kusa,growing aquatic plants and moss terrestrial in bowls on wood etc Have a check on Tashi Amano on Internet for mosses grown in aquariums inspired by nature and Japanese rock gardens.Aquarist gardeners often use yogurt to get moss growing

Here in the States, there was just a Growing a Greener World program detailing how to transplant and grow moss. You might get some useful tips from that, too, Bealyuk.