The smartest time to start rebellion is when the faction you will rebel against is already at war. You can do this by attacking a caravan of another kingdom before rebelling. You also need a good economy, so set up velvet dyeworks in towns where they turn a profit. At least 1 town or castle will do, because a good town gives you 2000+ denars per month and allows you to stick your troops in there. Remember; if you want to rebel, don't get villages, because if you rebel then, the village will not come over to your control.