due to my brother not having the luck of having Froyo on his phone I took a look at it and hacked the newst YouTube app to work with Eclair. I had to remove two calls and add android.util.base64 which was introduced with Froyo. However, it should work flawlessly. If you encounter any problems, feel free to post here along with a little description and if possible a logcat dump of the exception.
You have to remove the default YouTube app before you can install this one over.
Using ADB Shell this should just work:
adb shell rm system/app/YouTube.apk
adb uninstall com.google.android.youtube
then you can just install it over using the package manager or with adb (adb install YouTube_signed.apk).
Hope this helps, enjoy the re-designed Youtube app!