There is a Sine Wave Generator demo using PSoC 6 - https://www.cypress.com/documentation/code-examples/ce220924-psoc-6-mcu-vdac-sine-wave-generator-using-dma
I believe the method is basically same with the one for triangle wave generator.
I have found this example, but how can I have more than one frequency without messing up with the clock? Do I need to have a dynamic LUT generator or something of the sort?
Yes, you need a dynamic LUT generator, or something like that for more than one frequency.