best dairy-free yogurt for meat marinade (Biriyani)
In a marinade it is the enzymes and acids in yoghurt which are the important factor so a non-dairy substitute may not work well. 

Probably the best approach would be to use an oil and spice marinade. As biryani is a fairly dry dish the yogurt is probably less essential in contributing to a thick sauce as it might be in other recipes. 

Much will also depend on the cut of meat that you are using, yoghurt is especially good at tenderising cuts which can be tough or dry so you might consider using a more tender or fatty cut that usual, for example use chicken thigh instead of breast for moisture and adjust the marinate to suit eg add an acid (lemon juice, vinegar or tomato paste) for tougher cuts and a fat or oil for dryer ones.