I like to believe in alternative timelines. You go back in time kill your father prior to you being born then you just shoot off into an alternate timeline where you didn't exist.
Then you go into a different timeline where you didn't exist to kill your father, and are born again.
Actually there is no need for alternate timelines, and the Grandfather Paradox.
In Quantum Mechanics, there is a technique called Sum over Histories. In this, if you want to find the path that a particle took, then you add up all the possible paths that the particle might have taken. With light this is always the geodesic because if it followed a different path then it would not be the shortest path and so would have taken longer.
This is an important point, you only consider the
possible paths that the particle took, not all the paths that exist.
Now, if you apply this to the entire universe and time travel, then one of two things becomes apparent:
1) There is a finite number of paths that all the particles in the universe can take between the two events (departure and arrival events).
2) These two events are fixed.
What this means is that there is no way that the particles in the universe could have a sum over histories that prevent the Time Traveller from going back in time if they have actually travelled in time.
So there is no way that this Sum over Histories will allow the Grandfather Paradox, but it does allow a non-certain future, to particular degree. Events that do not influence the time traveller's journey back will be free to take whatever "path" they like.
So while killing your grandfather will be impossible, killing your cousin would not.