Maybe have it send them a daily email with links and thumbnails of the past 24 puppies.

The email would preferably contain the image itself - an hourly shot of happiness. On my own site, I offer hourly/daily options for alerts, and a surprising percentage opt for hourly - I think you could do the same. It would get expensive using a third party mailing service like sendgrid - just sending mail from your server via Exim is pretty easy and costs nothing extra.

I have a feeling you could get a surprising number of subscribers, especially since the puppies would be super-forwardable...

Some digital picture frames will accept an RSS feed. Why not make your site able to automatically update such a frame every hour?

Are there any companies out there offering RSS based image feeds, intended for such devices? One can imagine a digital frame hanging on a wall and the owner can subscribe to themed RSS streams. Owners might be householders, or companies looking for attractive wall art. A set of free streams could be offered, based on the Commons. There could also be paid or ad supported streams, based on proprietary images.

If you use HTML email, you can check if the last one was viewed -- and wait until it has before sending out a new email. A person might get 5 in an afternoon and one overnight.