I don't know whether they still make them, but there used to be a product called "Nipguards" or something like that, specially designed for the purpose.
I personally used normal strip elastoplast cut to length, particularly when I used to race in a club vest which had 3 seams which joined right on my nipple!!!!
Usually I just find that it's a bit of a problem if I've not been running for a while, especially if it is windy and raining, but after a few months of regular running they toughen up.