There are signs leading to additional parking at another parking lot, with a driveway entering from Madera Rd., on the same side of the street as the Reagan Library but West of Presidential Drive, near/at the intersection of Madera and Country Club Drive West.
I think the overflow lot is used on weekends when the library is busier.
Re the overflow parking at Madera and Country Club West, shuttles run between there and the Library, so it looks to be pretty convenient. The gates are closed when I go by at 7:30, but I think they open around 10:00 during the summer.