A skinny pig diet is the same as a regular guinea pigs diet. The biggest difference is the amount they eat.
Skinny pigs have a faster metabolism so they have to eat more.

Skinny Pig Pellets
I like to mix several high quality timothy hay based guinea pig pellets together. The package should read 20% crude protein and 16% fiber. It is important to buy the guinea pig food pellets in small quantity so that it get used before the Vitamin C in the pellets breaks down. Vitamin C degrades after 90 days so always check the use by date.
Keep the unused portion in the freezer to keep the Vitamin C stable. Never buy guinea pig food in bulk bin as you have no way to know how old it is.

Timothy Hay
Timothy hay is a very important part of their diet and needs to be available all the time; It should make up the bulk of there diet. Alfalfa hay can be offered to guinea pigs that are six moths and younger. Once they are full grown they should not be offered the alfalfa hay as it is too rich.
Hay should be stored out in the open in a clean dry area.

Fresh Veggies
Fresh vegetables are another way you ensure that your skinny pig is getting enough Vitamin C. Some of the fresh foods that can be given are:
An orange slice can be given be given once a week. More than that can that can lead to soresin the skinny pigs months.
Uneaten fresh food should be removed the next morning, you do not want it rotting in the cage.
Skinny pigs should have fresh clean water available at all times. The easiest way to do this is with a water bottle. Water bowls can get bedding and other cage debris in their water as they run and play. Cleaning the water bottle weekly is an often over looked important detail. With out regular cleaning bacteria can build up in the ball and spout and spread illness.