The whole point of a company supporting nonprofits is to impact the communities where they operate and do business. The Amazon Smile program was a brilliant way to distribute funding where customers thought it was needed the most…for example my PTA. These funds will be really missed, especially by public schools. I just cringe reading that Amazon thinks it’s spreading their impact too thin. They just don’t like the idea of lack of their own oversight as to how these funds are spent…and having to trust their customers and the nonprofit recipients.
So now let's focus on solutions. Check out ShopRaise, which has a similar micro-philanthropy program as Amazon Smile but with a broader set of retailers. Thanks to DonorPerfect for calling this to my attention. Nonprofits, register yourselves for this program and then promote it enthusiastically to your donor base. It's quite hard to change donor behavior so I encourage you to develop a consistent and persistent way to communicate this program to your community.
P.S. This is a best fit for your nonprofit if you believe your donors would put your organization as their top philanthropic priority. Otherwise this may not be worth the effort.