1. Nouns for Annoyment include annoy, annoyance, annoyances, annoyaunce, annoyaunces, annoyer, annoyers, annoyingness, Annoyments, annoys and Annoyment

2. Announcement, announcer, annoy, annoyance, Annoyancer, annoyer, annoyful, annoying, annoyingly, annoyingness

3. The Oxford English dictionary, gives only a dozen synonyms for annoyer and most are either Scottish (traik and skelf), or obsolete or rare (noyer, Annoyancer and galler), with the exceptions of annoyer, vexer and nuisance: therefore it is a true shame there is no such word in English.