A DishPro Plus 44, also called a DPP44, which is about $150 - $200.
However: All LNBF's must be either DishPro, SuperDish 121, SuperDish 105, or DishPro Plus. (Basically, you can not use Legacy LNBF, which are those that do not have a Black DP on the backside.)
If the LNBF setup for the 119 and 110 is a Twin, then you will run two cables to the switch, as you would if it was 2 separate DP LNBF.
EDIT:
The above is the basics, let us know the receiver type, and I or someone else may have some additional info for you. Also, this switch has a power inverter.