Simulating mouse clicks at specific screen coordinates

Question

I would like to be able to bind some keys to mouse clicks done in specific locations. For example: when I press F1 I should get a left mouse click at coordinates 300x350, F2 at 600x350 and so on. Even better if this could be bound to a specific window application so that coordinates could be relative to it instead of the base desktop.

Is there a software which allows this?

ADDITION:

Ok autohotkey is great but I have problems with my particular setup. Quoting my comment below:

I'm using it with an old game (championship manager 01/02) which runs in windowed mode (and I have to set win98 compatibility for it to run): I can get the mouse to move but no click goes to the application

I have read this FAQ but it didn't help, this is the script I tried:

SendMode Play
SetKeyDelay, 0, 50, Play

F1::Click 42, 191
F2::ControlSend ahk_class main, Click, Championship Manager 01/02

Still no luck: pointer moves but no click goes through.

Answer 1

http://www.autohotkey.com/ (and its clones) provide such feature. you want to use especially the "Click"-Command:

Clicks a mouse button at the specified coordinates. It can also hold down a mouse button, turn the mouse wheel, or move the mouse.