Tried sites like retailmenot, etc.
Yes, the "deals" page on Amtrak site has plenty of discounts, you'll see standard discounts, weekly specials, advertised specials etc., and there are also coupon codes floating around like the ones you may have seen on Retailnot, I usually use
Join Amtrak's frequent rider program. It works like an airlines program except it's more liberal with incentive perks.
Can I ask why you're asking this question on the Long Beach NY Forum? Amtrak doesn't travel to Long Beach.