There's a Constant family in the 1910 Census in East Orange, New Jersey, which might be of interest. Their address was 197 North 19th Street.
Constant, Leslie I., head, male, white, age 32, married once for four years, b. New York, parents b. New York, occupation - operator, printing office, rents home
wife Mary, white, age 29, married once for four years, mother of 2 children - both living, b. Ireland, parents b. Ireland, immigrated 1905, no occupation
son Carlisle B., white, age 3, b. New York, father b. New York, mother b. Ireland
daughter Myra I., white, age 9 months, father b. New York, mother b. Ireland
The age looks off from what you have, but any chance that could be your Mary Priscilla?