SongBook+ supports all foot pedals that either simulate an external keyboard (e.g. Cursor up/down) or can send MIDI signals (ControlChange or NoteOn/Off) to the iPad.
Here you can find a list of foot pedal manufacturers (in alphabetical order) that offer foot pedals compatible with SongBook+:
AirTurn (www.airturn.com), e.g. AirTurn DUO, QUAD, DIGIT, PEDpro, BT200S-2/4/6 (Manual1, Manual2)
Coda Music Technologies (www.codamusictech.com), e.g. STOMP Bluetooth Pedal (Manual)
IK Multimedia (www.ikmultimedia.com), e.g. iRig Blueboard, iRig Blueturn (Manual1, Manual2)
PageFlip (www.pageflip.com) e.g. Cicada, Butterfly, Firefly, Dragonfly (Manual)
Positive Grid (www.positivegrid.com), e.g. BT2, BT4 (Manual)
Strich Music, e.g. BT-FP2 (Manual)