Austin - As I read your problem it is pretty much as follows.
1 - You use non-standard tunings on a guitar.
2 - You create your own arrangements of tunes / chords using fingerings which may be completely individual to you.
3 - You need a method for noting down what you have done.
4 - You are not interested in having "the dots" in either standard musical notation or tablature. That is NOT your requirement.
5 - What you DO want is a method of typing out the lyrics of a song, then adding your (possibly invented) chord shapes above each lyric line.
6 - You would like to be able to do this using your computer, to give a neat printed output which you can also save as a computer file and maybe modify at a later date.

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The main problem which you are up against is that computer programmes tend to be designed to do a particular job well, but if that isn't what you want, they can be worse then useless. I suspect that there isn't one designed to do quite what you want.

I would go for a solution similar to that suggested by Nick_, creating fingerboard diagrams which you can insert into a word processed document.

My suggestion would be to use Open Office, partly because it is Free Software, partly because it runs on Windows, Linux, Macintosh and other computer systems, but mostly because it only took me about fifteen minutes on Open Office to produce a result similar to what I think you are asking.

Open office is a free download which installs as a bunch of linked applications including wordprocessor, spreadsheet, database, onscreen presentations and a structured drawing package.
The useful thing about structured drawing is that it is made from elements which you can individually alter without changing the rest of your picture. It is incredibly easy to do straight lines and dots, which is what you need for fingering diagrams.

First download and install OpenOffice.Org (if you use a Windows PC I would recommend Portable Apps, a suite of software which will run from a USB stick, but will also install on a PC without adding crud to the registry).

Start Open Offic and open a new document in "Draw". This will give you a blank canvas for your chord diagram. Go to the menu at the top and find View/Grid. You need to see the grid, so check "Display Grid" and "Snap to Grid". Your blank page should now be covered with tiny dots. As "Snap" is enabled, when you draw a straight line, the ends will go to the nearest grid point, perfect for drawing evenly spaced horizontal or vertical lines.
Find the "Line Drawing" tool (symbols at bottom of screen) to Draw your "strings", 6 for guitar, 4 for mandolin etc. - how long depends on the number of fret positions you need to notate. I drew strings horizontally, with a grid dot spacing between each string, but you could do it vertically like Nick_ did. Frets are lines across the strings, I found spacing at every 4th grid point worked neatly.
To add fingering, find the "Ellipse" tool, which will draw you a circle. The grid snap points are at corners of a square surrounding your circle (rectangle for ellipse), so if your circle fills 2 grid points square, when moved, it will snap to a position where it covers a "string" line.

You can copy and paste individual elements, or group them together so they behave as a single element. This would help when creating a set of chords.

Once a chord is made, you can select the diagram and copy it to clipboard. Once in clipboard, you can go to an Open Office "Write" wordprocessor document and paste your diagram into it. You will need to resize the diagram, but that is not difficult (right click on diagram and find menu item for Position and Size).

Type in a few lines of lyric, leaving enough spacing between your lines to allow for the chord diagram, size the diagram to fit, move it to where it aligns and Bob's your Uncle!

Remember that you can save your chord diagrams (or blank fretboard diagrams ready to add spots) as Draw documents ready to create new tunings and new custom chords.

Hope that helps.

Quack!
Geoff the Duck.