How does one deflate weekly price data? It seems the highest-frequency consumer price index (CPI) data available is monthly. How does one convert weekly or daily price data into real prices?
You don’t. CPI is a proxy for the fantastical concept of a real price. Any measure will have theoretical implications (Australia’s CPI makes some very funny housing assumptions, for example).

As the measure is a proxy for a theorised but unreachable category, and as the measure is only available at its noted frequencies you can’t create a line. Part of the measure is its frequency. 

This is impossible for two reasons:


proxies are just that
a measure which is grounded in theoretical assumptions and produced with a frequency can’t be resolved smaller than that frequency


You might look into producing a new measure acting as a proxy with a desired frequency, but only state agents and historians tend to go about these windmill fights.