In case someone else has the same problem, here's how I solved it:
I added the following line to /etc/modprobe.conf:
options cx88xx card=4
Then, dmesg looks like:
cx2388x v4l2 driver version 0.0.5 loaded
ACPI: PCI Interrupt 0000:01:01.0[A] -> GSI 22 (level, low) -> IRQ 21
CORE cx88[0]: subsystem: 1002:00f9, board: ATI TV Wonder Pro [card=4,insmod opti
on]
TV tuner 44 at 0x1fe, Radio tuner -1 at 0x1fe
cx88[0]/0: found at 0000:01:01.0, rev: 5, irq: 21, latency: 64, mmio: 0xfd000000
tuner 1-0060: All bytes are equal. It is not a TEA5767
tuner 1-0060: chip found @ 0xc0 (cx88[0])
tuner 1-0060: type set to 44 (Philips 4 in 1 (ATI TV Wonder Pro/Conexant))
cx88[0]/0: registered device video0 [v4l2]
cx88[0]/0: registered device vbi0