Describe the noise? Too high, too low, or just changing randomly? How much is it changing? A few mV of noise or all over the scale?
Fig 2 needs a ceramic or tantalum cap from Vdd to Vss, and it must be as close to the ADC as possible.
Be aware the MCP3201 loses accuracy if CLK is below 10kHz.
And of course review your code and verify the timing is being met. Be aware that the PIC samples pins in a different part of its instruction cycle than when it updates outputs, so a port write for the clk immediately followed by a port read is not one instruction cycle apart, timewise. When all else fails, add some NOPs in there.