There are four new Rochester newspapers on NYS Historic Newspapers but you may not be able to read them as they are all in German. Also, the earliest of the newspapers uses the Fraktur typescript which takes some getting used to. Usually you can search the newspapers on this website but it doesn’t come up with “hits” because of the Fraktur typescript. So you would have to search the early newspapers by date.
There are some deaths recorded in these newspapers but usually just the death date without any list of relatives.
The earliest of these German newspapers is Rochester Beobachter which was first published in 1851 but the earliest issue available is 1858. This was a weekly newspaper until 1870.
Bebachter became the daily newspaper Rochester Taglicher Beobachter in 1871 and the last available issue online is from 1883.
Then there is a big gap before the online issues of Rochester Abendpost start in 1906. Sometime in the 1950s that newspaper stopped using Fraktur type. The online run stops when the newspaper stopped being published in 1967.
The last new newspaper is Deutscher Wochenspiegel. That newspaper was a weekly published from 1967 – 1978. It doesn’t appear to have any local news, just national and world news.