Do you have exposed rafter tails? Or do you have a soffett?
If you have exposed rafter tails, you can sister on to these and extend your roof out about three feet before you will need to add columns for support.
This is a very easy process. Then you will need to deck this and then shingle it.
Now, if you have soffets, then you can use those metal hangers to attach the overhang joists to and again go out only about two feet in this case.
The more I think of it, not knowing your DIY experience level, you might want to have this done. I would estimate that the project would cost about $75 in material and I would charge about $150 in labor. This is for a three foot overhand w/o supports or columns.