Amazon Subscribe and Save already offers this service: http://www.amazon.com/Health-Personal-Care-Subscribe-Store/b...
Suppose you were doing this without computers or the web. Customers filled out a paper order form and you then fulfilled their standing orders. This is very similar to what Schwann's and diaper services do now, and what milk trucks did when I was a kid. 75% of the problems you need to solve will be in old-fashioned logistics: purchasing, warehousing, picking, packing, shipping. Almost all of the remaining work will be customer service: returns, fixing mistakes, handling late deliveries and billing issues, etc.
Now add a web site to place and track orders to the business. It is a tiny part of the work required to launch and doesn't change any of the back-end "brick and mortar" stuff.
Amazon has the infrastructure in place to do both the hard (logistics/fulfillment/customer service) parts and the easy (web site) part. If you think this is something you can crank out in a weekend with a Ruby on Rails book good luck.
You should also look at Diapers.com and Soap.com which was recently acquired by Amazon. http://finance.fortune.cnn.com/2010/11/06/amazon-to-buy-diap...
It's basically a direct-to-consumer marketplace for manufacturers.
