If they don't mind a rough ride, they could do it. I saw a couple there mountain biking on the trail parallel to us. They seemed to be moving along alright. It might be a bit technical though. Swampy parts are usually traversed using raised wooden decking. We parked in the lower parking lot. There is an upper one as well that we did not hike.
My fiancee and I went there over the weekend, and there are lots of trails, but the ones we hiked at least, were not bike friendly. They were very narrow, rocky and very overgrown. At times, we didn't feel like we were on a trail at all. The park seemed pretty big though so maybe we missed the easier trails. I think the nearby Sprague Creek Park is much more bike/kid friendly and also has playgrounds and picnic areas.
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