What are you asking them to do? If you just want to shoot right there,
simply ask and tell them what you will do with the images. Then don't shoot
immediately (they'll probably subconsciously pose), wait a few minutes, let
them relax.
If you want more, follow them for the day, pose in the studio. Have some
cards printed, to show you are serious (if not a professional) and have a
few meetings before the shoot.

Ex.
Excuse me, my name is Gary, I am a photographer out of Allentown. I am
shooting some photos for myself and the way you are sitting (eating,
standing, etc.) is very interesting (odd, exquisite, etc.) and I would love
to take a few photos of you. Would you mind?

Or

Excuse me, my name is Gary, I am a photographer out of Allentown. I am
shooting a series on beautiful black women (indian, older, rugged men, etc)
for a series for my portfolio (a client, posters, etc.) and I would love to
take a few photos of you at my studio. Would you mind?
Here is my card with my e-mail and phone, please call me and we will discuss
the shoot.

If they say no and are not interested, just thank them and let it go.

Works for me.