Possible communication solutions - TM1628 Keypad module (in DVD Players, etc)

i am finding it difficult to read and write to the chip through SPI

With an appropriate circuit it's pretty standard SPI. How did you connect it to the Arduino?

Was wondering if i could use a fairly standard reliable way to do this.

The reliable way to do this is using GPIOs. If that's too slow for you, please specify what speed you need.