There are several sites that offer online subscriptions to digital images of newspapers. Make certain though that if the site says it has newspapers from 1890-1900 that it has every issue published. Some sites upload images in "chunks" and coverage from 1890 through 1900 (or any set of years) may be spotty. There may be months where only a few days are covered and those days are apparently random.
Determine if the newspaper you are searching was weekly or daily as well as that also makes a difference. Not all old issues of newspapers survived to be microfilmed, but make certain you know what specific issues you are (and are NOT) searching when you query an image database.