I think most people are like me when it comes to emojis - we have 5-10 emojis that we use all the time and we hardly ever use anything else.
SwiftKey tries to suggest the next emoji and it often gets it right but I think it could be way better and faster if you added a Favorites tab to the emoji picker (next to the Suggested, Recent, Faces, Flags and so on). You could let the user add emojis to it by long-pressing them and then selecting 'Add to favorites' from a dropdown or with some sort of drag and drop.
That way each user could pick the emojis they use the most, put them in an order that works for them and save some time every time they need an emoji.
For you it would mean 1 a small UI adjustment in the tabs, 2 storing an additional array of about 10 elements for each user, containing the IDs/Unicode for each emoji and 3 adding the long-press functionality and the drop down.
Additionally, you could add an extra field in the Settings that would let us pick the default emojis tab. So for instance, user A could open the emoji picker and see their favorites while user B could open it and see the Recent tab by default.