The programmers should create a Wordpress plugin that let WordPress site owners create affiliate programs selling whatever products they want. The affiliate program allows customers to accept Bitcoin.
To make a plugin like this is a complex project because you need a VPS to run your bitcoin node somewhere, and that isn't cheap at all, just sear for VPS with 250Gb disk space and you will see what are i'm talking about.
And as other users say, that service already exists.
But i don't think you need a plugin for an affiliate program, what you need is a link API to know what customers buy X product. If what you want is to accept bitcoins you don't need an API you can do that posting the bitcoin addy on the site.