It's not an easy task, is it?
I tend to think one starting-point would be modeling behavior. The group that needs allies (whichever group that happens to be) should have members from its ranks willing to share their personal stories of specific interpersonal ways, from their perspectives and memories, in which allyship has touched them.
This will most likely resonate with wannabe-allies...but also with people who are on the fence about whether they're willing to pursue allyship...plus even people who are pretty sure they're already allies but want to always be reevaluating for self-improvement.