what "copper coins" are you hoping to differentiate from silver coins? If you mean large cents, then no, they read too high, and will mimic silver coins. But if you meant small cents (wheaties), then be aware that they are very difficult to tell apart from silver dimes. Yes you can tell silver quarters and halves apart from pennies with a lot of TID machines, but pennies to dimes is a much closer range on the TID scale.
The Explorers (especially the Exp II), as Larry says, is a good machine for TID's at depth. And I actually found the Whites Eagle SLII to be good at differentiating silver dimes from copper pennies. But the depth isn't what explorers get, and ... of course ... those clear-cut TID differences start to fade when you add depth and/or minerals to the soil.
But for turf-hunting, if you put a lot of time into the Exp. II to gain audio experience (listening for the particular "fluty" high pitch), it will almost get to where you can call the difference between silver and copper.
Be aware that this is for if you're talking places where the depths and ages are stratified (which is how turf generally is). But if you're talking other types sites (plowed fields, the beach, relic sites, etc..) where depth has no correlation to age, then all bets are off. You're going to have to dig the pennies if you want the silver dimes.