Write really unique ideas. Again, it’s MUCH easier to get something cut if it’s a great, unique idea. Dig deeper for cool, original ideas. But still, be very carefully about the fine line between being “unique” and being “weird”. The second one can be a turn off for the publishers.
Write with artists. Writing with artists not only increase your chances of a cut. It also makes you more attractive to publishers. If you come in with some artist relationships already in place, the publisher knows that they’ve got a better shot at making their money back because you are likely to get cuts on those artists’ albums.
Fill a niche that they don’t have. A common mistake for a writer is to try to work with a publisher who publishes songs similar to the ones they write. The problem with that strategy is that the publisher probably already has writers who do what you do. Try to find a publisher in the genre that you write that DOESN’T have a writer like you. If you can fill a niche, then you have a much better chance with a publisher.
Be versatile. Don’t just write one style or type of song. The more different types of artists you have songs for, the more attractive you are to a publisher. If you only write one style the publisher knows that YOU will be out of luck once that type of song is out of style. Diversify your portfolio. Write all kinds of things! If you can do these things consistently, you’ve got an exponentially better chance at finding a publisher who will invest in you.