I dislike the current head of my dynasty, can I arrange an accident for him?

Just keep throwing him in harms way. Hunts, get into as many fights as possible, piss off the natives, go crusading at every chance. That should up the odds nicely. There's gamey ways to do it like Rodolfo stated, but who would do that? ;)

ways I do that (legally):

• Really mistreat someone (like your wife), hopefully they'll start a plot to kill you.
• Put yourself in every battle you do, try to lose them ;)

In a more 'cheaty' way, you probably can load the game as one of your counts/dukes and select the plot to kill the liege :) then go back to yourself and wait until they succeed

One of the most reliable ways is to try and assassinate someone with very high intrigue. They will discover your assassin, and then they are very likely to send an assassin after you. If they fail, or don't send an assassin, just try again. Conveniently, after you die the reputation hit from assassinations disappear.

You can also commit suicide. This option is available in your decision tab, if your character has the "depressed" trait. I'm uncertain when this was introduced; I don't think it was possible in 1.0.