I think many people do not have a full sense of what a church is and what it does. To many a church is a place to go on Sunday to hear a sermon, when they consider the costs they only account for the salaries of the pastors and the cost of the building.
The church is much more than that, or should be. The church is the people, the needs of the people, if someone is jobless in your congregation does the church step in to help, or does your church rely on certain generous members. Is your church involved in other Christian ministries like food banks, homeless shelters, tract distrobution, discipling, supporting missionaries here and abroad? Those are all roles of the church.
The church in Antioch was not told to TITHE, but they did support Paul's missions financially at times. The churches in Asia were not told to TITHE but Paul did go and accept a love offering for the church in Jerusalem on their behalf.
The churches also took care of the poor who couldn't take care of themselves, they appointed Stephen and Philip and others to work with Widows and the fringe of their flock. Their work of feeding widows also required funding and sacrifice on behalf of the congregation.
In the New Testament we see two models of giving. Jesus had a money bag where he and his disciples kept a communal fund for ministering to the poor. Donations that came into Jesus' ministry went into that money bag (which Judas helped himself to liberally). Despite Judas' abuse this was a specific model for the way that a church is run, money is collected and used for the needs.
Jesus was also given a donkey to ride into Jerusalem, an upper room celebrate the Passover, and a tomb by single contributers. There is a place for direct one-on-one administration of funds to needs in the bible, so if someone in your congregation has an extra un-used car and there is someone else with a need this could be an example to follow.
The church in the New Testament doesn't TITHE, but they are much more liberal with their money, sharing it together as Jesus did with the money bag, but also in single contributions.
We also have the model of Barnabus who sold his property for the sake of the church, and then became a missionary with Paul, discipling Paul, Mark, Luke and others along the way.