This is a good idea. Many of the films I would recommend are very old. But they should be found on DVD or VHS.
I have some suggestion for now, Two little forgetten jewels:
"Wanda", Barbara Loden (wife of Elie Kazan) made only this little film in a Cassavetes style, 1970
DVD.
"Little fugitive" "A lyrical serio-comedy from the writing/directing team of Ray Ashley, Morris Engel and Ruth Orkin, The Little Fugitive stars young Richie Andrusco as Joey Norton, a seven-year-old Brooklynite left in the care of his 12-year-old brother Lennie (Ricky Brewster)" 1954, DVD, b/w.