let me understand this...
Is the Sirius radio portable and you want to be able to plug it into a wall jack in the kitchen, have the audio signal go to the basement to a receiver I assume, and then have the audio play through the speakers in the kitchen?
The simple solution is to run 2 coax from the kitchen to the basement. Trim out the coax at each end with a wallplate that has female RCA jacks.
At the kitchen, plug in your analog audio from the sirius. At the basement run an audio cable from the wallplate to the appropriate input on the receiver.
That wallplate in the kitchen can now be used for any audio source you want to play thru the receiver (i.e. an iPod).
If the receiver is in the basement you will have to manually control the source input by going downstairs every time. I would suggest running a cat5 from the basement to your volume control. This will alllow you to add an IR receiver or better yet get a volume control with a built-in IR receiver.
To be really slick, instead of a volume control install an Elan Ole'2. This will give you complete control of the system in the basement as well as local control of the volume in the kitchen.