Yes it's possible.
You will need Dolffhin Live, bigui, or EA graphocs editor.
I would suggest Dolffin live.
You can find it here.
http://www.nba2kstuff.org/flipper/
I don't have NBA Live 06, so it may be a little different from 07.
Go to xcommon in the C:/Program files/EA Sports/NBA Live 06
Then open the VIV file xcoach.
Or something like that.
Export one of the faces from one of the fsh files, make sure you export the fsh file too.
Edit it with Adobe Photoshop to your liking.
Then open the FSH file you got the texture from with FshX, you can find it in the Genaral Downloads section.
Import your texture, save, then place the FSH file in you NBA Live 06 sgsm folder.
It should show the face you edited.
2 things,
1. I think you have to do some DBF Editing to make a new coach. I don't know how, sorry.
2. The FSH file will have the coaches first two letters in the beginning 2 letters, like, Lebron James, (just an example cause I don't know any coaches)
If he was a coach, the FSH would be named: lejames, and lejamesr, would be the reflection of him you see on the court.
Hope that helps,
-JR