To contend or strive, especially on even terms or with success: coping with child rearing and a full-time job.
To contend with difficulties and act to overcome them: "Facing unprecedented problems, the Federal Reserve of the early 1930s couldn't cope"(Robert J. Samuelson).
[Middle English copen, coupen, to strike, from Old French couper, from Vulgar Latin *colpāre, from Late Latin colpus, blow; see coup.] cop'er n.