moss lawn yes it is possible to create a moss lawn, this is most commonly done in Japaneses style gardens. In addition to moss there is also a number of other alternatives to grass which are

Moss lawns – To create a moss lawn you need to create ideal conditions that are opposite to that of a traditional grass lawn. You need to create a compacted soil to hold moisture. This can be done with a roller or compacting plate available from a tool hire centre. The soil ideally needs to be lean so remove and existing turf and do not add any fertilizers. With regards to the moss itself you are best to try to establish the moss as plugs 6 to 10 per square metre. The largest job is weeding, in Japanese style gardens with moss lawns the weeding was always carried out with paraquat-based weedkiller which is a contact based weed killer killing most weeds and grasses but not the moss. However this chemical has now been banned but some experimentation with other contact weed killers you should find one that has a similar effect or you could spot treat or hand weed.
With regards to finding the moss we could have a look around our suppliers and see if any of them could help I image it would not be that expensive to source.

Calamine Lawns – calamine lawns have traditional been the alternative to grass lawns and are best grown from plugs or small pot plants 6 to 10 to the square metre the biggest problem being the establishment which requires a lot of weeding.

Sedum Lawns – Sedum more commonly used on the roofs of building to produce a green roof is another alternative to grass and again the key in the early stages is weeding to allow the plants to establish to create a sward. Sedums are available as pot plants plugs and mats similar to turf.