Oh! How does one go about figuring that out? I have very limited knowledge in the field, so all that occurs to me when you say "suggestions API" is the feature, where a site comes up with suggestions, as you type. Like Wikipedia, and IMDb, as you mentioned. But I'm guessing there's something more to it, since Game of Thrones Wikia and A Wiki of Ice and Fire do give suggestions, when you search.
I'd want to know how to figure it out, so I don't make more suggestions, without checking if the sites are actual possibilities for you to implement.