I've been using push notifications with the Beejive app on the iPhone, which got updated recently and it works great. But when using AIM on a Mac, it can be kind of frustrating since you cannot be logged into two Machines at the same time with AIM. So, if you are logged into the iPhone (even in the background), and you connect with iChat or Adium on the Mac, then AIM sends you a message at both places asking you which Machine you want to be connected from.

To me, it would be ideal to only receive notifications on my Mac when I'm using my Mac, and only receive notifications on the iPhone when I'm using my iPhone. This seems to be pretty much attainable when using Google chat (over Jabber) instead of AIM (and thus requiring Beejive instead of AIM on the iPhone). If you are logged into Jabber from two Machines, and someone chats you, it will send the messages to all machines that are logged in, until you reply from one machine. At that point, Google chat will only send messages to that machine, until it logs out. Once you log out, it will then send it to the other machine again.

So the hint is as follows: in Beejive on the iPhone, in Settings, set it to keep you logged in for 24 hours. Then on the Mac, download Adium (instead of iChat -- the desired level of control is not available in iChat), and add your Google account. In Adium's preferences, under the Status tab, set it so that after some period of inactivity (10 minutes perhaps), it switches your account to offline.

Then, when you are using your Mac, Google chat messages will get pushed to Adium (and to your iPhone as well, until you reply to one from your Mac), but after the period of inactivity on your Mac, it will switch you to offline, and those messages will get sent to the iPhone instead. Once you start using your Mac again, message will get pushed there again.