Avrilaceous is not a word, unless you are Banvillaceous.
After some debate (see attached Google search), the general consensus is that the word has been coined by Banville to refer to Avril, whom the reader first meets on page 55. She is an incidental character who serves to illustrate the narrator's unreliable memory.
He remembers, dimly, her face 'was sprinkled all over with tiny freckles'. On page 129 the narrator refers to his own greying hair that is flecked with Avrilaceous freckles. And on page 157, when a robin appears, he remembers that Avril's freckles reminded him of something else.