Prosaic has great advice :)
The whole industry is moving away from "Studio" portraits and such for families. It is always easier to get more natural shouts in either a familiar setting (your home) or outdoors or in a place that is significant to your family.
You could contact your local collage or even Community Arts Council and inquire about local photographers who do "location" portraits. They might have some suggestions for young photographers who are trying to build their portfolio.
Also there might be an option to barter services or goods, especially with photographers who want to set-up a business (sometimes the left brained business stuff is a challenge) Maybe they would just be grateful for some home cooked meals.
Once you have the photos (make sure you get them on disk and a decent file size) you can turn to Groupon and take advantage of their online deals and create yourself a photobook, canavas print or any of the 100 other products out there.
All that being said, as a professional photographer, it does hurt to hear things like *I can't imagine paying for portraits in the age of digital cameras* There is a lot going on besides simply pressing the shutter. A good photographer will know proper framing, composition, what you should wear to get the best look, styling, specific photography techniques, lighting, be able to direct and instruct you, make you feel comfortable. Plus have a wider variety of equipment and editing capabilities and get those amazing shots that someone just pressing a shutter won't be able to do.
Good Luck :)