Electronic – Clean DC power supply from a dirty souce

Add capacitors between each power rail and ground. They'll act like short circuits to the high-frequency noise. I see that you have one between the -9 V rail and ground-- that's a good start.

The type of capacitor you use can make a difference. Electrolytic caps, for example, are relatively cheap, but they only deliver their rated capacitance at low frequencies, so they're not as good for filtering out high-frequency noise. I've had good luck with tantalum capacitors in this kind of application, but be careful that you don't plug them in backwards, as they will explode. Be double careful with the negative rail, because "backwards" might be the reverse of what you think. For both rails, you want the plus on the capacitor connected to the more positive terminal, which is ground for the -9 V rail.

My guess is that it may be the cheap Crossplay supply, which is coupling (capacitive from the mains side) it's switching frequency onto the signal/PC/mains ground.
I would try using another (preferably better quality) supply of the same voltage rating (with same or better current rating) to see if things improve. Or you could try a ferrite bead clamped on the cable of the current supply if you have one handy.
If you have any means of isolating the Crossplay from the PC (e.g. little 1:1 audio transformer or similar between Crossplay/PC) then that should also do the trick if it is as suspected.

EDIT - guess 2 :-)

If it's not the Crossplay supply, then it's almost certainly the PC supply. In this case I think the easiest way to sort it is probably to buy the little isolator you link to, rather than trying to filter. These things are very handy to have lying around if you are into audio in any way.
In the meantime you could maybe try things like plugging the PC supply into the same socket as the Crossplay if it isn't already, or using shorter/thicker cables.
Audio noise problems can be quite difficult to diagnose, but IME (I have a small recording studio) an isolator will usually fix things, and often the easiest option.
One more thing - if your Crossplay happens to have a differential input (unlikely I guess) then use that.