If you're hunting specifically for the halcyon bird as the central creature, the pickings are surprisingly slim. It's almost always a symbol, a fleeting reference, or a guild name rather than the star of the show. I scoured my shelves and my Goodreads lists and kept hitting dead ends.
The one that kept coming up was the 'Halcyon Fairy' in Disney's 'The Sword in the Stone', but that's a movie scene, not a book, and it's just a brief moment of mythic reference. The other major one is Shakespeare's 'The Tempest'. He wrote that line 'Gods, I am quiet now as these halcyon birds,' but again, it's a metaphor, not a character. It feels like fantasy authors tend to default to phoenixes or hippogriffs for their elemental avian needs, leaving the halcyon in the poetic reference bin where it's beautiful but never gets to stretch its wings as an actual plot-driving creature.
Maybe the best you can find is in some niche Arthurian retellings or in the background of certain epic poems where the 'halcyon days' are a literal, magical period of calm conjured by the bird's presence, but even those are more atmospheric than central. It's a weird gap in the market, honestly. Someone should write that book.