I love those newspapers. You can search by name, which yields results, but what has helped me immensely is the county correspondents. My folks lived in the Monarch district and the Monarch correspondents loved that family because they show up all the time, so I was able to get all kinds of info on their day to day life, which is really fun. I wish other newspapers were like that!
But if your folks were mentioned in one of the localities -- Craig, Mound City, Forest City, Maitland (rare), Naples, etc. -- then you might just start looking through the paper, week by week, for that locality, and you should be able to find more about them. The search is through text-recognition software, which often garbles stuff, so the search definitely doesn't catch everything.
Also look at The County Paper -- it's the predecessor to the Holt County Sentinel in the late 1800's. They published it for only a few years but it might add a little family info, who knows?
I wish the LOC would get the Savannah Reporter online and then I'd really be in business!