There's no hardware-based I2C or SPI support built into the 630xx/631xx parts, so you will have to manually toggle GPIO pins with firmware to implement an I2C or SPI interface.
This can be done successfully. You will need to know the desired bit timing and switch the GPIO modes between resistive and open drain modes to drive the pins HIGH/LOW accordingly. Unfortunately, we do not have any example code to illustrate this method.
You should also be aware that, for new low-speed designs, Cypress recommends using the enCore II family. The enCore II family offers a lot more features over the CY630xx. Some of the added features are crystal-less oscillator (no external oscillator needed), SPI compatible (both Master and Slave), internal 3.3V regulator, wake-up circuit (external RC circuit is not needed), pull-up resistors, Combi USB and PS/2 interfaces supported. All of these add up to a lower system cost.
For more information on this part, please visit our web site at: www.cypress.com (choose Products--> USB--> Low-speed).