For many reasons it might be best to keep your Dish Network subscription system separate from your FTA system and intall a second DBS dish (an old 18" D* would do) for the music at 119..
For starters, what kind of LNB does your subscribed Dish Network dish have intalled on it? If it is a one-piece LNB (the 110 and 119 "eyes" are part of the same unit) you will have trouble hooking it up to anything other than a Dish Network receiver.
If it is a one-piece DP LNB (DishPro) it can be done, but since the LNB has a built-in DiSEqC switch, it is a real pain to include a second dish. Also, DP LNBs use stacked frequencies, all H transponders are stacked at frequencies above the V ones, so you have to edit your TP list (again, a pain). If it is a one-piece "Legacy" LNB, its totally useless to a FTA reciever since the integrated switch is proprietary.
If you have one of the old style Dish500 dishes with 2 separate LNBs, you're in business. Assuming you have dual-output LNBs (and you only have one TV with Dish Network), you'd run a cable from the unused output of the 119 LNB to an input on a DiSEqC switch, run the output from your G-10R dish's LNB to another input on the DiSEqC switch, and run the output from the switch to your receiver. Then you'd have to setup your receiver to "look" at the appropriate ports on your switch for the satellite you're watching.
Of course, if you have more than one TV hooked up to Dish Network, you'd be out of luck there as both outputs on your Dish 119 LNB would be used. You could split one output, but then you'd have to use DC blocks and only one of your recievers (either the Dish one or the FTA one) would control polarity (with a DC block on the other "slave" receiver to prevent it from sending out power to the LNB)..
If you decide to install a separate dish just for the music, I recommend going a step further and installing a "REAL" FTA dish (30" or more) on a motor. That way you can get everything else on the other birds (IA-5, AMC 1, 4, SBS-6, etc.) up there as well.