In addition to Tottenham winger Bale and Sunderland’s Vaughan, Celtic’s Joe Ledley, Cardiff City defender Darcy Blake and Neal Eardley of Blackpool are also absent for Coleman ahead of his second game in charge.
The ex-Coventry City manager has included Liverpool forward Craig Bellamy in the 22-man squad, however, despite doubts over the 32-year old’s desire to continue playing for Wales following the death of Gary Speed.
"I've included him [Bellamy] in my squad," Coleman told BBC Sport. "I wouldn't have included him if I didn't think he wanted to continue with us [Wales].
"If Craig wants to make a statement about what he intends to do, maybe that will quash all the rumours.
"But he is very, very much a part of us going forward about this next campaign and we will have a better chance of doing something special with Craig rather than without him.
"Until he tells me otherwise I'm going to continue to pick him."
Aston Villa defender James Collins missed out on a place in the squad after falling behind Ashley Williams and Blake in the Wales pecking order.
"James Collins has lost his place with Ashley Williams really being really the mainstay and Darcy Blake has done well at international level," continued Coleman.
"They haven't done anything wrong there. James has had a long hard season, he has had a few niggles.
"I know all about James. I'm not going to learn anything from him."
Instead, Coleman has opted for untried talent in a plan to experiment with line-ups in the friendly in New York. Nottingham Forest’s Joel Lynch could make his international debut while Swansea’s Ashley Richards, and Blackburn youngster Adam Henley are also among the new faces.
But Coleman reassured his senior players that they are not out of the picture by any means.
"I may learn other things from players I don't know so well," he explained.
"It's not me burning bridges with the experienced players. On the contrary - they are very much part of our make-up and squad going forward."