I'm not familiar with parse implementation. However if you use the standard GCM method to send a push message then the notification is created in your service code. So you can customize it in any way you like.
Parse does not use a special icon but the icon you put in the application files- in object/res/drawable put the icon you want with the name "icon.png". I have it with two applications and each time parse sends a push notification it appears with the specific application's icon.