The LaTeX engine (xelatex) does not natively support raster fonts (required for coloured noto emoji). lualatex is an alternative engine, but breaks other things. Really, we can use a hack to replace unicode characters with images that are pre-rendered emoji glyphs.
It's possible to render out the glyphs using freetype or PIL. Both of these cases require special care. Thankfully, there is also emojicdn that serves emoji PNGs as a service.