Manually managing songs and deleting from playlist
Speaking for iOS 6 (not necessarily older versions):


Open Music.app
Select "Playlists" tab.
Create a new Playlist and put a few songs in there.
Sync your iPhone to to your computer (Wifi or USB)
Make sure iTunes is configured to sync your music and choose "Selected playlists, artists, albums, and genres
My experience was that the playlist I created was automatically selected under "Playlists" in the Music tab of iTunes. If it isn't, select it.
You can now put any song you would like in there and sync.


While it doesn't automatically sync every time a change is made, any time you sync it will reflect changes made on your device. For example, put 10 songs into your new playlist and sync with your iPhone. Then, go into your iPhone and delete a few of those songs out. Sync with iTunes. They shouldn't be in the playlist on iTunes anymore. 

I have personally performed the steps to ensure they work. It's not 100% automatic, but with Wifi sync, it is almost that way.