Affiliate programs directories are one way to find affiliate programs, another method is large affiliate networks that provide the platform for dozens or even hundreds of advertisers. The third option is to check the target website itself for a reference to their affiliate program. Websites, which offer an affiliate program often, have a link titled "affiliate program", "affiliates", "referral program" or "webmasters" somewhere on their website, usually in the footer or "About" section of the site.
Even if all those methods seem to indicate that a site does not have an affiliate program, could it still be the case that there exists a non-public affiliate program. The only way to find out for sure, is to contact the site owner directly and ask.