Is there an IDE that I can load on a Blackberry, E71, or an iPhone?
Not that I know of, typically you'll develop apps on a desktop machine (PC/MAC whatever) and download/control the application on the phone. Also I don't think Java is available on a standard (non-cracked) iPhone.
There was a palm based C compiler. I had some trouble finding it though, but it's called OnBoard-C. It didn't exactly have an IDE, it compiled notes. Considering there's a lack of embedded compilers, I'd be surprised to find full embedded IDEs. Oh... I recall there being a Scheme or Lisp too.
This maybe premature but, congrats, you just found a market niche.
Apple released iPhone SDK for XCode a while back, check out developer.apple.com and Nokia also release their own SDK check out forum.nokia.com
But for pure Java Midlet goodness, i would recommend Netbeans (netbeans.org) their netbeans mobile application editor is a gem, second to none.
To answer your question, i don't think any phone is powerful enough to compile and test the code on themselves, so no ...