What type of livery do you need? If you go to Central saddlery (near Avonbridge), the guys in the feed shop are really helpful and always have some contacts.
There's also always loads of adverts on the door for livery.
Central is definitely your best bet, they are close to Linlithgow and will know of pretty much all the yards in your area. Willie and Norrie (I think that's their names?!) in the feed room are very helpful and like I said, lots of adverts with numbers to call on the back of the door of the main shop.
Have you tried Dot Smart place, they have a few stables I think and lots of grazing. They do DIY and full livery, I know the woman who runs the place ands he's really nice.
What about Fieldings? It's East Whitburn so a bit further, but might see you through?
Sorry you did PM me about this but I haven't really been able to come up with anything.
I'm from the North East and have to say there is way more choice up there, both in terms of livery and competition venues etc. It's not great down here to be honest.
If you pick up equiads there are a few livery places in Linlithgow area. Good luck, it's a nightmare when you have more than 1. Got 3 and had the same issues.