[Music niche] How would you do this?

Traditionally, unknown songwriters approach music publishers to see if they are looking for songs to pitch to specific artists etc, and if yes, the publisher would allow the songwriter to send over a demo. In turn the publisher would pitch the songs to the labels and artists. If recorded, the revenue would then be split. You can still go this route but I suggest reading publications such as this one first.

2014 Songwriter's Market: James Duncan:...
These types of books will educate you on the many do's and dont's of the biz, and also has contact information etc. Online you will also find tons of free info.

That's not an affiliate link by the way, so I won't earn my 20 cents if you click on it.

In the last few years the Internet has of course also opened up many opportunities, thus you can go through websites such as:

Music Producers | Music Managers and Artists | Musicxray Opportunities

These types of sites charge a fee, but they allow for unknown songwriters to send music over to artists and their labels etc for consideration.

Hope this helps.