I copied this from the Morewinemaking.com website manual on yeast pairing, they don't list Barbera directly, but for Rose suggest:
Rhône 4600: Complex aromatics along with strawberry, pear and pineapple. Enhances mouthfeel and volume. Great single strain choice or as a blending component.
ICV-GRE: Stable fresh fruit characters, along with high fore-mouth volume enhancement. Good as a single-strain or as a blending component.
ICV-D21: Enhances mouthfeel while maintaining acid-ity for bright, fresh fruit in the final wine. Useful as a blending component to freshen-up hot climate/high pH fruit.
W15: Bright fruit with heavy mouthfeel makes W15 a good single strain-selection by itself, or as a blending component.
71B: “Fruit salad” character, long-lived aromas from production of esters and higher alcohols. Can metabolize up to 30% of the malic acid in a must.
I have used the Rhone 4600 on St. Vincent and Chambourcin Rose and find it produces a very nice wine. I might avoid 71B, since I want all the acidity I can get in a rose.