If the pics are heavy gague, and well fitted, nothing more than putting them on snugly works for my autoharp playing (30+ years). The light, easy to bend ones were not inclined to stay put.
It takes some time, and the use of needle-nosed pliers, to get them adjusted to get the right angle/shape for a snug fit. Now, they are so well worn that they obviously only fit on one specific finger. My current set for my best 'harp have outlasted 3 plastic thumb picks that wear down; dont like a metal thumb pick. This set has lasted for at least 7 years. I'm still breaking in a set for my second harp.
I have occasionally tucked scraps of small post-its inside them when I've got a sore hangnail/ cuticle, to protect the skin some.
Good luck getting the picks to work for you.

Joanne in Cleveland