What is the best time to offer discounts on products?

Seasonal discounts as well :)

I usually offer discounts around major holidays like Black Friday/Cyber Monday, Christmas, Valentine's Day, etc. Also doing end of season sales to clear out older inventory works well. My advice is to plan ahead, promote heavily to your email list and social, and make the discounts compelling enough to drive action (20%+ off). It's also smart to do some special 24-hour flash sales throughout the year to spike revenue. Just don't discount too frequently or you'll train customers to wait for sales and devalue your brand. Hope this helps!

New product launches and loyalty rewards are what I like the most

From my experience offering discounts right before a product update or launch generates a lot of buzz.

Maybe a coupon after a purchase to make them want to come again?

I think it depends on analyzing customer behavior. Have you looked into when your audience is most active or engaged with your product.

Offering discounts right after customers have shown interest in my product whether through browsing or cart abandonment is a great way to convert that interest into sales.

For me, holidays work best people are already in a shopping mindset.

I've found that offering discounts at the end of the month works well when people get paid.

Back-to-school season has always been a win for me especially when targeting students or parents.