Hi,
This is an issue I work with a lot. Over the last few years it's become a lot harder to earn natural links for my own sites and for client sites, as people move onto social networks, and away from blogging etc.
So what's the solution?
You could try paying journalists/writers. However, it will be expensive, particularly for any reasonable quality links. And real journalists don't tend to sell paid links - it tends to be the lower level contributors in blog and guest post sections, who are quite often found out (I know various media owners who purged their sites of contributors selling links, wiping out £1000s in paid links...)
So what can you do?
Create something amazing and linkable.
It could be something that's incredibly valuable and useful. A guide to all the related local services if someone is moving to the area for example (e.g. house movers, house sitters, useful local organisations etc).
It could be something that's newsworthy. For example, every gift and experience site went through a phase of creating the most outlandish and bizarre gifts they could, themed around current news and holidays. Things like 'the most expensive valentine's day hamper in the world', for example.
You could work with local organisations (e.g. charities), or sponsor a local team of some kind.
That's for starters. Obviously if you want more specific ideas, that's the sort of thing I'm paid to do for a range of businesses!