Who sings the old song that goes...

Stay with me... stay with me.

It was featured on Ghost Whisper on Friday the 23rd.

It might be rock steady by bad company

Maybe...

Rod Stewart | Stay With Me lyrics

In the morning
Don't say you love me
Cause Ill only kick you out of the door

I know your name is rita
Cause your perfum smelling sweeter
Since when I saw you down on the floor
Guitar

Won't need too much pursuading
I don't mean to sound degrading
But with a face like that
You got nothing to laugh about

Red lips hair and fingernails
I hear you're a mean old jezabel
Lets go up stairs and read my tarot cards

Stay with me
Stay with me
For tonight you better stay with me

Stay with me
Stay with me
For tonight you better stay with me

So in the morning
Please don't say you love me
Cause you know Ill only kick you out the door

Yea Ill pay your cab fare home
You can even use my best colonge
Just don't be here in the morning when I wake up

Stay with me
Stay with me
Cause tonight you better stay with me
Sit down, get up, get down

Stay with me
Stay with me
Cause tonight your going stay with me
Hey, what's your name again
Oh no, get down, wooo

Probably not it because it is not old, but Josh Gracin sings "Stay With Me" (Brass Bed song)

"I'm going to start watching this show just so I can answer all these Ghost Whisperer songs!