@BComptonNHL - NHL.com writer and will tweet about every major islander move. Occasionally some smaller details but a good source for big announcements.
@ehornick - Isles statistician (don't know if he is the official team one but he posts a crazy amount interesting stats throughout the season)
@BDGallof - columnist for CBS covering the Islanders. He tweets A TON.
@Schultz88 - current writer and editor for IPB (islanderspointblank.com), great website as well
@ChrisBottaNHL - founder of IPB and former PR man for the Isles. Writes for the sports business journal and the NYT. Not frequent but great information on the team
Those are just a few of many people who regularly tweet legitimate info about the islanders. Follow them and look at who they re-tweet and **** and you can find way more people.
I know they aren't "beat writers" but they regularly have great legitimate information on the team. Sorry if that wasn't what you were looking for.