1. Rent your car from an off-airport location
If you have a rental of more than a few days, it will probably be worth it for you to take the SuperShuttle or a cab to a nearby off-airport rental location. You can return the car at the airport location at no additional cost. Send one adult to get the car while the kids play at one of the airport's play centers or have a snack at one of the restaurants.
Here's a map of the closest off-airport locations for Enterprise, Budget, Avis, and Hertz.
I checked rates for comparable cars at on- and off-airport locations of a few companies. The car itself is approximately the same cost, but a week-long rental racked up 15% more in taxes ($50-$75 depending on what you rent) PLUS various facility fees and surcharges to the tune of another $20. You'd probably rather spend your vacation money on actual fun instead of taxes and fees. (One person could take the SuperShuttle for $13-$17 to one of these off-airport locations.)
2. Rent car seats from Sweet Pea Baby Rentals instead of the car rental agencies
Most car rental agencies charge $9-$12/day for child seats. On a week long rental, that could cost you upwards of $90 per seat including the airport tax, and who knows what the condition will be. I can almost guarantee you that seat isn't even worth $90 brand new.
With us it's $55/wk plus 6.3% tax on a premium Britax car seat, and only $30-$38/wk on booster and infant seats. It's guaranteed to be clean, sanitized, safe, and include all instructions for installation. We also give a 10% discount on the second or more of the same item. We can deliver all your rental items wherever you rent your car, or can deliver to multiple locations like your car rental location for your car seats, and your accomodations with everything else.
3. Take the hotel shuttle from the airport and rent your car there
Most of our hotels and resorts offer a free airport shuttle and an on-site car rental service at their location. If they don't have an on site rental counter, most of the off-airport rental car locations will pick you up free at your hotel and take you to their facility. Again, you can return the car to the airport facility at no additional charge. So, if you don't need the car right away, this is a great option and can even cut days off your rental.
4. Use coupon codes or bid on Priceline.com
Here's a pretty good compilation of coupon codes for rental cars. You can also make a confirmed reservation in advance, then a few days before you trip, bid for something less than the rate you booked on priceline.com. Then, just cancel your other reservation if you get a better deal. If you're not picky about what company you get, this can be a good option. You can only bid for cars at the airport locations though.