mm wrote:

I have a standard POTS line for a phone and if the extensions in the
basement and main bedroom are plugged in, the phones in the kitchen
and office play WBAL AM radio, 1090.

Can I make a simple filter to get rid of this? What size capacitor
would I use (in parallel with the phone I presume)?

Unless that radio station is very close to you, the problem is likely
caused by a corroded connection. You can filter it out, but if you
can find the connection and clean it you'll solve it too. One
problem with this is that the problem may exist internally in one
of the phones. But you can track that down easily by unplugging
phones.

This happens all the time with music equipment. Poor connections
on cables start tuning local radio stations. All you really need
to make an old fashion crystal radio is a diode. Corroded connections
can do a fine job at this. Then the capacitance and inductance
in the rest of the amplifier functions as the tuning stage.