While tzatziki is the preferred sauce in traditional gyros, 
you can always substitute for hummus to try something different. 
Feel free to use any kind of hummus you desire in this recipe
Ingredients:

4 pita bread rounds
1 cup of hummus of choice
1 large onion, chopped
2 medium tomatoes, diced
Crumbled feta cheese
Slices of gyro meat(eyeball it, but about 4-8 slices per sandwich depending on the size of the pita)
Dried oregano, to garnish

Place a piece of aluminum foil down on a flat surface. 
Put a piece of pita bread in the center of the foil. 
Spread a generous amount of hummus across the middle of the pita bread. 
Top with chopped onion and tomato and then add the beef gyro meat. 
Top with feta cheese and drop another spoonful of hummus over the top, if desired. 
Sprinkle some oregano over all the ingredients.

Roll the gyro and wrap it in aluminum foil so it can hold the shape. 
Repeat until you've used up all the pita bread.
Feel free to also add some tzatziki if you want