Haiti perhaps? I know DR has trogon as it's national bird, not so sure about Haiti and can't think of an exw species from there although.Thanks @J I N X .
This country lacks much of the biodiversity of its larger neighbours, having only a handful of endemic species, one of which is extinct in the wild.
It is one of 2 countries in the world, both from the same region, to have a national bird from this small but distinctive bird order.