The SNES2 didn't include RGB or S-video output, for reasons known only to Nintendo. Luckily it's really easy to get RGB output from this system.
This mod is fairly easy, although it requires a bit of planning and a steady hand. You will need to attach three wires (R, G and B) to pins 20, 22 and 24 of chip U7. The chip is clearly marked and located just behind the cartridge slot of the SNES. New! There is no Composite Sync output from the newstyle SNES. If you want to add this, you will need to run a line from pin 7 of the chip U7 to the sync output of the SNES. (Thanks to Raymond Day for that little tidbit.)
Shown in the top picture is the video chip. First, remove the heatshield, then attach the four wires. Run them under where the heatshield would be, and then tuck them through a hole in the motherboard allowing them to reach the bottom of the board. You should attach the Red, Green, and Blue wires to pins 20, 22, and 24 (as well as another wire for Composite Sync to pin 7) of this chip.
The RGB signal itself is very strong. It is recommended that you run each video signal through a resistor to tone them down depending on your monitor or personal taste (somewhere between 75 to 125 ohms). 75ohm resistors seem to be the 'definitive' value judging by the last two revisions of the original model SNES that also used the same 'S-RGB A' video chip used in the SNES2 (Motherboard codes of these revisions are: SNS-CPU-RGB-01, SNS-CPU-RGB-02 and SNS-CPU-1CHIP-01) So use one 75ohm resistor in series on each line - Red, Green and Blue.
It is also recommended that you use a normal NTSC SNES RGB cable, i.e. one with 220uF capacitors inside on the Red, Green, and Blue lines (+ leg towards console, - leg towards display) The capacitors are usually already inside any Nintendo Scart cable you buy, but its always wise to double check. The capacitors are there to remove the 1V DC offset in the RGB signal - although many TV/Monitors will still display the RGB picture fine without them they are strongly recommended to help prevent any damage occuring to less tolerant displays.
In the bottom picture is where the four wires are attached to the bottom of the SNES2 AV port. In this picture the white wire (for Composite Sync) obscures where the red wire is attached for pin 1 but all four wires are attached. A clear insulating compound was used to help protect the connections and exposed wire.
Note that the SNES2 Chroma Encoder chip, which is labelled the same on the board (U4) is NOT the same chip as the original SNES. This one's RGB inputs from the now integrated PPU2 chip are on different pins.
There are more pictures and data on the old page.
This is a picture taken with a XRGB-3 using this mod. Composite sync and 100ohm resistors on the RGB lines were used, as well as an original Super Famicom RGB cable: