Event Pokemon that have Happy Hour or Celebrate are not Shiny. Is there a way to get a shiny Pokemon that can use this?
In Japan only, a shiny Magikarp, Ho-Oh, and Rayquaza with Celebrate were released in 2015 (Magikarp) and 2016 (Ho-Oh and Rayquaza). Additionally, you can teach Celebrate to a shiny Smeargle using Sketch.
Sources: mostly went through Serebii's Celebrate page and checked the event dex of each Pokemon listed. Also cross-referenced with Bulbapedia.