Custer State Park [1] is open to mountain biking nearly everywhere in the park unless restrictions are established for conservation or trail restoration purposes. Check with the visitors centers [2] for any closings. The trails listed here are suitable for both hikers and bikers.
Mountain bike rentals ($10/hour, $30/half-day, $50/day) are available in the park at both Legion Lake Lodge and at the State Game Lodge [3]. Mountain biking guides for the park are available at the park visitors centers.
Bring water with you as there is no water available along the trails. Do not drink from any of the streams.
Bikers must yield to both horseback riders and hikers. Remember to keep your distance from buffalo and other wildlife, and be careful of poison ivy along the trail.
Links:
[1] http://www.moon.com/destinations/mt-rushmore-the-black-hills/the-southern-hills/custer-state-park
[2] http://www.moon.com/destinations/mt-rushmore-the-black-hills/the-southern-hills/custer-state-park/visitors-centers
[3] http://www.moon.com/destinations/mt-rushmore-the-black-hills/the-southern-hills/custer-state-park/accommodations
[4] http://www.moon.com/destinations/mt-rushmore-the-black-hills/the-southern-hills/custer-state-park/outdoor-recreation/mountain-biking/grace-coolidge-
[5] http://www.moon.com/destinations/mt-rushmore-the-black-hills/the-southern-hills/custer-state-park/outdoor-recreation/mountain-biking/centennial-trai
[6] http://www.moon.com/destinations/mt-rushmore-the-black-hills/the-southern-hills/custer-state-park/outdoor-recreation/mountain-biking/big-tree-robber