These are some comments about what you should look for, not a true answer. Also mind that 'ancient Greece' may mean many centuries (and different countries, places and colonies). This question may not have a single answer valid for all.
Do not think on Temples as churches - people did not go there mainly to pray. There were built for sacrifices: the priests went inside to offer a sacrifice and read the omens, while the people waited outside the colonnade. Then the priest would exit and tell the people if the omens were good, indicating that the gods accepted their sacrifice.
Even temple architecture is not appropriate for large gatherings. Look at these floor plants of Greek temples. The colonnades occupy a lot of space, and the sacrifices were offered in the quite small innermost rooms - often there is only space for a few priests. BTW, the figure also shows very small temples, you could look for specific info about them.
This kind of floor plan is not appropriate for the Christian mass. The Christian church wanted to offer the Eucharistic sacrifice in the front of the whole congregation, besides having the priest deliver his sermon to the people. When the Christians looked for an architectural model for their churches, they choose the Basilica, a civil building appropriate for speeches, where a speaker in an elevated position could address an indoor assistance, and not the temple + colonnade model.
So you have to look for which sacrifices were offered in smaller communities.
What would be a small community? Many Greek states had slavery-based economies. Thus a smaller 'community' may be a larger house for the master/slave owner surrounded by buildings used by his slaves, other clan members, clients and animals. He may be the chief of the clan (what the Romans would call 'gens').
Even if it is a village of freemen, many of them would be related or belong to the same clan.
In both cases I expect that most of the sacrifices would be offered to their familiar (tribal or gens) deities and their own direct ancestors as filial duties. This could be made on altars placed on a room in their own houses (specially the house of the patriarch), or over the tombs of their ancestors (as it is done in some Greek plays).
Therefore you should first look for info about the familiar or ancestral cult in your target period/place.
If you are worried about separate temple buildings, you should look for customs and calendars about larger or more important sacrifices over communal concerns such as harvests, or to the higher Gods such as Zeus, etc. It is quite possible that these would focus on larger communities, as the main patriarchs/officials of the larger clans or city states would be there.
All these observations are very general. A classical book about the ancient Greek worldview and religion is The Ancient City by Foustel de Coulanges. I warn you that reading this book make reading Greek plays less surprising, as you understand how they think and already know what they must do.