Can someone please recommend me a tool to alert me when a specific person (or a group) comes online?
There is no way to do this with Facebook's online interface, however since Facebook now allows you to log in via any XMPP client, you could use any of a number of XMPP clients which have alert functionality.
One of the clients Facebook recommends is Pidgin; I use it regularly and it has "buddy pounces" which will alert you in various ways (window flashing, noise, message dialog) when a specific person or people come online. You can configure it to alert you any time they log on, or only the next time. You can also configure it to alert you when they return from being idle, etc. This would probably be the easiest approach. Pidgin is available for free on Windows or Linux, and Adium is built on the same libraries and is available for Mac OS X.
If you want to log when people sign on and off without being at your computer to notice, you can enable the setting to log all status changes to the system log. This will log all status changes, which includes changes from "offline" to "online", which allows you to see when people came online/offline. Obviously the computer does need to be online to do this.
I know if you use Meebo (online webapp) for instant messaging, you can log into Facebook chat and get alerts however you want, I think. Apparently Facebook released the chat's API, so you might find that you can log into Facebook chat from other IM clients, such as Pidgin or Trillian, and then simply configure it to alert you when a contact comes online.
Well, It's been a while since this question was made, but anyway, I've recently developed a Chrome extension that shows desktop notifications when a user comes online, you may want to check it out:
If you are using an Android Phone, you can use this https://play.google.com/store/apps/details?id=flashbang.apps.fbtrack
You can track your friends, and it will notify you when any of them come online.