We recently purchased a new car for my wife that has XM built in. But I would like to change it over to Sirius. Is there any way to incorporate the factory installed XM antenna into a Sirius radio without having to install a seperate antenna?

Depending on what vehicle it is, Sirius has a line of products called SiriusConnect which convert the vehicle's factory XM to Sirius. This one is for GM vehicles:

SiriusConnect Tuner for Class-2 Bus GM Vehicles - Shop Sirius (http://shop.sirius.com/edealinv/servlet/ExecMacro?nurl=control/StoreItem.vm&ctl_nbr=2640&siId=1910520&catParentID=24750&scId=24750&oldParentID=7870)

With my experience on GM vehicles, I have heard that you loose about 50% signal quality if you use an XM antenna for Sirius signal. I have a Chevy Uplander that has a factory antenna, but it has 2 cables, one for satellite signal and one for the terrestrial signal, and the two cables go into one connector. I found an adaptor that would plug into the factory connector and covert it so it would plug into the SiriusConnect tuner. But it cost $50 and the only company I found that sold it said they quit stocking it because people were complaining about the signal.

Well I spoke to soon. I just checked TssRadio and they have them back in stock and at a cheaper price.
Not sure what vehicle you have but these are for GM. One is for a single coax and the other is for the dual coax. You can use these with the SiriusConnect that scots mentioned about.

XM to SIRIUS Dual Input Antenna Adapter (XmToSirius) Description (http://www.tss-radio.com/sirius-dual-input-antenna-adapter-p-3910.html)

XM to SIRIUS Single Input Antenna Adapter (XmToSirius) Description (http://www.tss-radio.com/sirius-single-input-antenna-adapter-p-3883.html)

The SiriusConnect comes with a Sirus antenna.

The SiriusConnect comes with a Sirus antenna.
Yes, but the OP wants to use the factory installed XM antenna not the antenna that comes with the Sirius units.

Yes, but the OP wants to use the factory installed XM antenna not the antenna that comes with the Sirius units.

That is correct. The car is a 2005 Honda Accord. Do they make one for the Honda's??