What eclark says is the general solution, but recently I stumbled upon Keychain:
... a front-end to ssh-agent, allowing you to easily have one long-running ssh-agent process per system, rather than per login session. This dramatically reduces the number of times you need to enter your passphrase from once per new login session to once every time your local machine is rebooted.
More details are included at the link above (including security concerns), but it would allow a process (they give the example of cron, but any process should work) to use certain keys without having to know the passphrase.
You might consider this, as it would appear to be much more secure than a passphrase-less key.