screws through stucco into sheathing??

I am putting vinyl siding on the front of our house that presently has the rock style stucco on it.
I want to put furring strips, then siding right over top of the stucco, but I need a screw to go through the 1/2" furring strip, them self tap through the stucco, then into the plywood sheathing. Any ideas what I could use? I might try screws that are used for self tapping into cement flooring board (though isn't this cement board a lot softer than stucco?). I tried ordinary screws, and they don't want to penetrate the stucco? Any advice would be great! I don't want to have to drill a pilot hole each time I put in a screw!
Cory
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Cory Lechner wrote:

Yes. Jim McNamara does. He will be along anytime now to instruct you in this. He is an expert at everything in the entire universe. He's the Anti-Christ.
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The stucco is the rock style, so it is fairly even & level...

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