I guess you can connect a battery to CY8CKIT-042 between J1.2 (P4.VDD) and J1.5 (GND) pins to power the PSoC 4 device. However, all the peripherals on the kit may not be powered with that and only the PSoC 4 power domain would be active.
You can use a CR2032 3V coin-cell battery to start experimenting with. Take care while powering the PSoC 4 through P4.VDD pin as it would not have protection circuit and may damaged the kit if reversed/shorted.
Please refer to the kit Schematic for power domain details and refer to the PSoC 4 datasheet for complete range of Voltage and Current specifications.
BTW, checkout these Pioneer Kits which have coin-cell battery support by default.