My 8 year old son has been doing BJJ for a couple of months now. He keeps getting taking down by this simple maneuver: opponent's leg behind your leg trip.
Are the options just to sprawl out on time or grab the leg? Anything else?
The advice I'd give to an eight year old for preventing a Gracie-family-style kosotogake-makikomi would be limited.
There are more and better options, but for an eight-year-old, that's more than enough. They should be focusing on putting in and enjoying mat time instead of specific stand-up technical issues anyway. If the throw remains a problem after a few more months, the instructor should step in and provide tactical or technical advice.
For an 8 year old kid, keeping the distance is probably the best option. like robin and dave have mentioned.
If they are looking to be a little more adventurous. o uchi gara, and uchi mata are both viable counters to a bjj style ko soto gaki/gari.
o uchi gar is in the first group, uchi mata in the second. both require a lot of practise for the timing, and are probably worth having your son work on, but not count on for a long time.
uchi mata will work a lot kil this video: http://www.youtube.com/watch?v=GpGzHiHNPQI
I can't find a video of o uchi gari as the counter. but basically as they are hooking their leg behind your leg, you turn and steer their upper body around, dragging that foot in a circle.
The inside leg trip is a more reliable takedown than the outside leg trip, but it's not popular in BJJ because the inside leg trip puts you in their guard, while the outside one at least gives you half mount. The inside leg trip is a natural counter to the outside leg trip, and in practice the inside leg trip tends to win (I'm not entirely sure if this is because it's favoured by wrestlers and they're way better at takedowns than BJJers, but I would expect if the outside leg trip had viability you'd see it in wrestling competitions as well).
To be able to get the outside leg trip, you need hip to hip contact, so fighting for control of the clinch to keep the hips apart will also entirely kill any chance of getting the outside leg trip.