Here is my suggestion about a new chess variant. I hope you would try it with your friends to see if it works.

Generating the immortal pieces:

 Throw two coins to decide the pieces ( Queen, rooks, bishops and knights ) that will become immortal. Only one type of pieces will be chosen. For example, rooks will become immortal if two heads turn up. In the case of two tails, knights will become immortal and so on. Once chosen, both sides will have the same immortal pieces.

Rules about immortal pieces: 

 1. They are immune from capture from the enemy pieces except the king. So, they are actually near-immortal pieces .

 2. They can check and checkmate.

 3. They can only capture pawns but not other pieces.