What current do the relays need? I offer a couple of shift register boards that might do the trick to sink current thru relay coils.
One uses TPIC6B595 and can control 96 outputs at up to 150mA per output.
A second uses shift registers to drive N-channel MOSFETs at 1 or more Amps, depending on how many are driven at one time. It is set up as 4 channels of 8 outputs, with each channel supporting 8 to 10A.
The first one has arduino controller built in, only an FTDI Basic or equivalent needs to be plugged on to download code into it. The second one needs a separate Arduino to control it. Both are easy to control, just blast one to however many bytes are needed to fill the shift registers being used.
http://www.crossroadsfencing.com/BobuinoRev17/
We've redone this one recently to use SMD transistors, resistors, caps, and LEDs. Very easy to daisychain the control signals with a 6-conductor ribbon cable.
I have a P-channel MOSFET version also, very heavy with the TO-220 package, and pricey as low Rds P-channel MOSFETs are more expensive.
Pretty good Rds with -4.5V gate drive, when you just gotta source current!
https://www.fairchildsemi.com/datasheets/ND/NDB6020P.pdf