How low is the lighting? Or, how many hours a day of sunlight does the area receive?

While some grasses do OK at 4 hours or even less of sun per day, the keyword there is "OK." And by OK, I mean...well, so-so. If coddled. All. The. Time. See creeping red fescue (which is green, not red).

For shaded areas, grasses are often not the best solution. A mulched area with shade perennials or low shrubs that can handle lower light levels might serve you better.

How wet is the area where you are having a problem growing grass. Grass may not be growing because it gets too much water.

You said it is on a hill, what is above this area and is this a natural drainage area. If it is you, may consider diverting the water in some other direction. Possibly a drain at the top of the slope. May be a drain that with the line running down the slope.

The area back there does remain fairly wet most of the spring and fall, but dry in summer. Isn't there grass that can grow in this type of wetter soil with lower sunlight?

poa trivialis will do well in shady areas that are wet. Depends on how far south you are. Where are you located.

Thanks! We're in Indianapolis, will it still grow here?

It's the "lower sunlight" issue that's still of concern even if you dry it out. And I'm sure others besides me will chime in on the wisdom of using P. trivialis as a lawn grass. Personally, I don't advise it as it won't stay put...and you won't approve of it elsewhere. :-)

Plus it doesn't tend to do very well during the summer, or when areas do dry out, so the combination of dry summers or drying the area out and using triv wouldn't work too well. Spring and fall would be OK.