This is more of a brainstorming session/life hack than an answer specific for academic, hopefully this can spark some more inputs. As a disclaimer, I identify with you as I am also working in the field of biostatistics and epidemiology, though I have not actively sought after extra income. However, I have always been a financial life junkie and I used to love to daydream how to be rich or at least to enjoy retirement with dignity. Here are some of my thoughts and, well, refined thoughts.
Saving = Income - Expenses
We should first recognize that you can save money by either getting more or spending less. Before going to get more, I'd recommend sitting down with your spouse and go over the financial situation. Here are a few exercises that I found easy to pick up, and once you have started, you may see if this route is good:
Create a happy matrix for your spending: Print out your credit card statement(s), item by item, grade how each of them makes you happy (Likert's scale, etc. you know the drill.) Identify things that are not contributing any satisfaction and avoid making the same purchase again. For those that truly make you happy, evaluate if you can cut back (usually, from all my reading, the culprit is often the $7.90 something Starbucks grande latte and a scone for the breakfast), or substitute with cheaper options such as shifting to other vendors or make them at home. I especially recommend everyone to check their credit card bill, bank bill, and cell phone bill: When I first started this routine, I found out that I have $280 sitting in my credit card as cash back! I just never claimed it.
Have an energy audit of your house: Most local government should be able to point you to some free energy audit service. They will evaluate your house's insulation, electricity usage, conditions of the heating system etc. and provide you a list of improvements and expected return on investment. For example, you can spend about $1,200 to inject foam in between inner and outer wall, and drop your heating bill by more than $200 per year. Other gadgets like motion sensing switch, smart thermostat, and CFL light bulbs may also help.
Take public transport or bike: I actually use this method. I don't drive and I live about 9 miles away from work. I commute on bike in spring, summer, and fall; and use subway in winter.
Commit to be green: This sounds like quite off. But I have come to realize that once you want to cut down on trash, you can't help but cut down on consumption. For example, I bring my travel mug and a collapsible box everywhere in case if I need to buy a drink or food. Since packaged food is automatically out of the equation (which are usually more expensive per weight), I save some money there. I also go to wet market or farmer's market for food, and I don't consume processed food. If I need an item I check out local flea market and freecycle websites (I give away stuff through freecycle as well.) For level 2 difficulty: Commit to be a vegetarian or vegan. Meatless lifestyle simplifies life tremendously.
Use your educator's identity: Many vendors provide discount to educators. Since you work in a university, you can flash your staff card and get some good saving here and there. I'd also encourage you to check with your university's benefit page. I got a 24% discount on my phone bill just because I filled in an extra form.
Then up a notch
If you have mortgages and complicated insurances, etc. Consider talking to a financial planner. Most of them can point you to some restructuring to make the system more streamlined. Simple things like grouping the insurance to one company can save monthly payment. I have even read about an extreme case that a couple actually ends up saving more by having one of them stopped working because the commute, childcare, and other expenses were eating into the take-home income so much.
Now, zoom out
I do understand that you value your biostatistics skills. But when it comes to making money, you don't have to only work on biostatistics. For me, after 9 hours of coding and reading outputs, I'd rather see something else. Once you have broken out from the box, you'll feel more liberated. Reassess your passions and hobbies, and see if you can pursue an instructor position somewhere. For example, personal trainer, yoga teacher, musical instrument teacher, handcraft, carpentry, gardening, etc.
On my own spare time, I write video game walkthroughs, and post them on various websites and my own wiki sites. In the walkthrough I put affiliated links to vendors and in the wiki I earn Google Ads money. Given I am not very prolific, I don't earn a lot, but I can usually pocket about $300-400 a year if I happen to have written a walkthrough for a popular game.
Finally, zoom back in
Now, back to your question. There are many ways a biostatistcian can expand their job repertoire. Here are some examples:
Consult your local classified websites such as Craigslist: Check for consultant type of jobs. You may even post an ad if you are so enticed. I used to do some consultation on and off as a student and got to charge $50 to $100 an hour.
Propose a course to local adult learning center: Most cities should have some adult learning centers the provide classes on hobbies or professional skills. Meet with the director and propose a course (on R, for example). You can build clientele and enlarge your social network as well.
Statistical editor and reader: You can also contact local editors and discuss on possibility to be an ad hoc statistical editor. I am actually working towards this direction. In my institution there are a lot of orphan data: grants ended, staff left, no body works on it and publishes the work. I found my niche of being a data undertaker, and I grew to be very interested in writing as well. Other than editors, you can also sell your skills to students who are writing their thesis. Most of their works can benefit by having a round of quantitative examination.
Look for an adjunct position: I know you don't want to, but I'd urge you to be a bit more adventurous on this option. Since online education is actually picking up traction, your skill in biostatistics and website building may actually be a good combination for some institutions looking for a way to move their program online. For remote course you usually just need to meet the student in the first 1-2 weeks or every other week, which can still preserve your flexible time table. Use online chat or billboard for office hour, give students feedback using track-changes, etc. You can do most of these at home.
I hope I didn't sound patronizing. But I wholeheartedly hope you may find some of these useful. I used to have mindset like you do, thinking of how to expand my income sources (I have my own expense and family in my home country to support), but after a few rounds of thinking, and sorting out what are the most important, I didn't feel like that any more. Now I make sure I have good pre-tax saving taken out first, save at least 10%, allocate money for family, allocate minimal expenses, keep about 5% or so for entertainment, buy used, give away or sell my own used goods, bike to work, stop all cable TV, lend to people on Kiva.org, simplify my closet, practice the motto of "buy the experience, don't buy the stuff"... etc. I realize that I still have enough, and I am not really sure what I was fussing about in the past. I'm happier, calmer, and definitely feeling clearer about what I want. And I certainly hope you'll be able to find your solution as well!