The easiest way to create a new part IS to start from an existing part. Whether the existing is in core or not. Drag the existing part to a sketch, then right click and choose Edit (new parts editor) from the menu. If the only thing you need to change is the PCB graphics, goto that view, then export; As image; SVG. Use whatever editor (like Inkscape) to make the changes, then File; Load image for view back in the parts editor. Save that as a new part, load it into your “mine” parts bin, and ready to go.
If I used the correct existing core part to walk through the steps as I was writing the above, all that is needed is to move one of the coil connector holes. You might also want to change properties and description for the new part.
These two sets of tutorials apply to the current versions of Fritzing (most of the others are for older versions of the software.) Using Eagle2Fritzing is more difficult yet (for starters you need a Fritzing development environment to build Eagle2Fritzing!) If you need a small number of parts, it is easier to convince one of us that know parts making to make them for you. That said we are always willing to help people to make parts as everyone benefits from more people willing and able to make parts.
Locating a Fritzing Part file, or asking for help