The best ways I've seen to promote affiliates is to make them contextually relevant. Instead of treating the affiliate like an ad, mention an affiliate's product or service when it makes sense within the context of your content.
For example, I share my affiliate code (“noodle”) for Libsyn, Blubrry, and Spreaker when I mention any of those companies within the context of talking about where to get media hosting. I don't take a “commercial break” from a random topic and then do an ad for my affiliate.
When an affiliate is contextually relevant, listeners and readers are far more likely to take action on it.
Also ensure you're following your local laws and disclosing the relationship.