The title is a good representation of what I want to do. Is there a standard way of testing out my chord progression so that I can hear it without having to write it down on a score? Writing out the notes of each chord is too slow and I am having trouble learning what each chord sounds like.
If you mean something like this...
My chords are: Am D Em C (or whatever)
...now I just want to hear them, then try this:
I think you can find many other apps like that for smartphones where you can select from rhythm styles and instruments. Basically, I think Apple's Garageband does all that stuff.
The is also a program called Band in a Box. I haven't used it, but my understanding is that it provides the same function to generate a rhythm section from a chord progression.
But, also some electric keyboards have harmony buttons that I think are supposed to "auto" harmonize a bass.
Another acoustic possibility is an autoharp.
Those things can help you along to quickly hear the chord changes, but eventually you want to get basic skills on keyboard or guitar to be able to play chords. You should also get a foundation in harmony so you can learn the terminology of chords and common functions. Try getting into a library and look at the harmony textbooks. In the meanwhile, from a pop/rock perspective, this site might help you: http://www.angelfire.com/fl4/moneychords/lesson.html. It lists a lot of very common chord progressions. My point is this: experiment with those chord playing apps, but also study chord patterns. Most songs follow common patterns.
On the other hand, if you mean you want an alternative to writing chords on music staves, maybe what you need is a guide to the short hand notations. There are basically two: roman numeral analysis and jazz chord symbols. I suppose you can add a third: Nashville number system. Those are all widely used chord progression short hands that don't require notation on music staves.