I made a Barney cake for my daughter's birthday a couple of years ago and used Americolor Electric Purple. IMO, that's the perfect Barney color. Here's a picture of the color I used.
Since you don't have access to Americolor, I guess you could try mixing the Wilton colors and see how you come out. Barney purple has a bit more red than blue. Just guessing, but maybe you could try rose pink with just a touch of blue?
Just want to add my 2 cents. When you mix the Wilton colors, especially the dark ones like red and blue, the icing can taste bitter if you use too much (I found that out the hard way once, had to throw out an entire batch of icing because it tasted so awful that I would never feed it to anyone). Just try mixing the color a little lighter than you want it and let it sit out for a while. The color will darken as it sits, you won't have to use as much of the paste and you will end up with a much better tasting icing (experience talking, LOL).