You need to show them that you can solve their problems.
The #1 mistake made by most applicants is that they keep talking about themselves: "here are my skills, here's what I've done, etc..."
Instead of talking about yourself, talk about them:
"You need someone who can jump right in; someone who can start working without making mistakes. You also don't have a lot of time for training. I can get started right away."
This is going to require some research. Follow the founders / managers on Twitter. Read their blog posts. Scan their error logs (if they're public). Find out where you're *needed* and highlight that.
Generally it's best to do this during the application process. If you've already sent in a cover letter and resume, it doesn't hurt to send a follow-up email that says: "I've been doing some research, and I think I've found some places I could be helpful."