What's the best way to track discount attribution across channels?

As an e-commerce manager, I'm struggling to understand which marketing channels are truly driving conversions through my discount campaigns. I need a systematic approach to track discount attribution accurately, ensuring I can measure the real impact of promotions across different platforms like email, social media, paid ads, and affiliate marketing. Without clear attribution, I'm essentially flying blind on the effectiveness of my promotional strategies and potentially wasting marketing budget on underperforming channels.