I actually think this should be the funding source. This is basically what Facebook is for as my very pregnant wife said as soon as she saw the site. But she was still pretty enthusiastic till she saw the 10$ cost. "Facebook it is!"
This might work, but the people getting the message need that value communicated. Cute dinosaur emails do not say 'I'm throwing money around'. The site would need a complete redo.
On the other hand the cute dinosaurs are very appealing right now. And this service is likely really cheap to run, and collects the names and emails of people, new parents, who will be purchasing lot of stuff right now... That's valuable and I think that's the revenue stream I'd go after.