How can I use a lower sample rate for songs on an older iPhone, in order to fit more songs?
There's an option to downrate the sample rate within iTunes when you sync to iDevices, however this has it's issues and advantages:


songs are reencoded on the fly during sync
the original sync will take a long time (in order of hours)
only songs needed to be synced will be re-encoded so choose your music carefully


This option is only available when your iDevice is connected.  Select your device from the iTunes left hand side bar, then choose the Summary section from the main window.

The option is labelled (in the English locale) as "Convert higher bit rate songs to..." as in the image below.

In current versions of iTunes, the Capacity bar at the bottom will resize to show your savings if you choose to sync.