In need of some advice!

I've got a client that has asked me to build very specific backlinks. The client is a Care Management phone application. They have a lot of contacts in the care industry and have therefore managed to secure a lot of backlinks from that sector. They've tasked me with building backlinks in the tech/app industry.

The niche is so small that I'm struggling to find websites that would be interested in the content that we are creating so am coming to the BHW community to ask - what would you do?

How would you go about finding genuine white-hat backlinks - currently emailing authors in the field isn't working out for me!