Is there a possibility to add a field such as "carrier choice" where I will be able include/exclude carriers for the coupon ?
Prestashop 1.6 (mean shipping->carriers in admin panel)
Do you mean make a product discount coupon that only works for certain carriers?
If so, yes, with a parent coupon:
Coupon A: product discount
Coupon B: shipping coupon where you select the specific carriers and set discount to 0
Coupon C: parent coupon where you add both coupons A and B and set process type to ONLY if all apply
Then give out Coupon C