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Some Anglican/Episcopal Churches have mid week and morning/evening prayer services. However since you said no Catholic Churches, you are probably not interested in Episcopalian. They are very similar to Catholic in worship and theology.
Most evangelical churches I know of (Baptist, Pentecostal (Assembly of God/Church of God) have Wednesday evening services. Many non-denominational evangelical churches also have Wednesday night services. Some mainline protestant churches like the United Methodist Church, Presbyterian Church in the United States, and the Evangelical Lutheran Church in America also have mid week services.