Hi John,
the Kirchenbucher are typically only for a specific town/city, so the KB
for Hannover that you looked at was just for the city, not the province -
which was pretty big. Without knowing the specific town your ancestor came
from, you may not be able to find out much further, especially since
"Peters" is a fairly common name widely distributed (today) throughout
Northern Germany.
Does the passenger manifest not give a home town?
The other place you might look is in the "Germans to America" series of
volumes, available at larger libraries - ask at your local library and they
should be able to tell you where the closest copy to you is. There are
some issues with the GTA series, some people say it's not 100%
accurate, but it is a source - treat it as something to be confirmed.
regards and good luck!
Art Dohrman