Where can I download recent precipitation data for Cape Town
It really depends on what you're looking for and what data formats you want to use. If you're looking for single location direct readings from rain gauges, you might have much better luck contacting the South Africa Weather Service (though this might not be free and is typically not 'Open' in the strictest sense of the word).

Some alternatives to that really depend on what you want (gauges, vs. radar estimates vs. homogenized estimates vs. composite products), the granularity (monthly, daily, hourly; observations or normalized climatologies), the spatial resolution (point locations, grids), and the format (Spreadsheets, GRIB, CF-compliant NetCDF, etc.). It's worth also noting that radar detection of precipitation didn't really become an employed standard until the 1980's (ref.)

For a few options that are open, I would suggest looking over what's available through the NSF's National Center for Atmospheric Research . The CMAP: CPC Merged Analysis of Precipitation or the 
GPCP (Monthly): Global Precipitation Climatology Project might work for you.