Here are 2 ways to get free 2 day shipping on Amazon.
join Amazon Mom's too. The program is targeted at parents of babies or toddlers but parents with children of any age can actually join too. Amazon Mom's get free 2 day shipping. Also you can save 30% off select diapers and wipes and 15% off most other items if you sign up for a subscription. The subscription program at Amazon is where they mail you a package every so many months. For example you can get a new box of diapers ever 1 or 2 months as you need them.
Note: the Amazon Prime benefits you get in these programs do NOT include all the benefits of paid Prime membership. You do not get the free online streaming video. There may be other benefits you don't get as well.