Regular emails with promotions can reconnect past shoppers with your business and attract them back based on what you;re promoting.
Pacific Magazines through their free Nexus program provides newsagents with a free email marketing platform. If you are a in Nexus you should be sending an email out every fortnight. Plus you should be seizing every opportunity to harvest customer email addresses. Pacific is happy for newsagents to promote anything using the free emails.
I’ve heard of plenty of email campaigns working for newsagents. I use them.