I have an iPhone app called "My Songbook - Lyrics & Chords" by Or Sharir. It's $1.99 in the iTunes store. I've only been using it for a couple of days, so I haven't had time to tryout all of the features. However, I've been able to download my cordpro files (i.e. files that have the ".pro" extention) directly into the app from my web based email account (you have to email yourself the files as an attachment, then access your account via the web browser within the app). There are a few other ways of downloading files into the app also, e.g. by ftp or if you have an online account where you can store your files. However, I could not access my Windows Live skydrive account using the browser within the app.
You can also surf over to this web site (cordie.com) using the browser and download songs directly from here. When I have more free time, I have to give that a try. It also has editing features, so you can edit the cordpro files to make corrections, etc. The song lyrics/chords display looks pretty cool and has an auto-scroll feature.
For more info., here's the link to the fellow who developed the app... http://sites.google.com/site/orsharirapps/mysongbook