Years ago, I looked for a website with the words and tunes for parts of davening, to provide guidance for parents who wanted to keep up with their children's day school curriculum. I found a Hebrew School which had parts of this available; I would post the link, but I have not been able to find it again since.
The other day, though, I received an email about a new site, which offers a service for davening as well as songs for Shabbos, and more. The site is Shir haLev. While there is much I would do differently on the site, and they definitely should post the words along with the tunes, this is a good start. I'd recommend checking it out.