Yb(Rh_{1-x}Co_{x})_{2}Si_{2} is a model system to address two challenging problems in the field of strongly correlated electron systems. The first is the intriguing competition between ferromagnetic (FM) and antiferromagnetic (AFM) order when approaching a magnetic quantum critical point (QCP). The second is the occurrence of magnetic order along a very hard crystalline electric field (CEF) direction, i.e., along the one with the smallest available magnetic moment. Here, we present a detailed study of the evolution of the magnetic order in this system from a FM state with moments along the very hard c direction at x=0.27 towards the yet unknown magnetic state at x=0. We first observe a transition towards an AFM canted state with decreasing x and then to a pure AFM state. This confirms that the QCP in YbRh_{2}Si_{2} is AFM, but the phase diagram is very similar to those observed in some inherently FM systems like NbFe_{2} and CeRuPO, which suggests that the basic underlying instability might be FM. Despite the huge CEF anisotropy the ordered moment retains a component along the c axis also in the AFM state. The huge CEF anisotropy in Yb(Rh_{1-x}Co_{x})_{2}Si_{2} excludes that this hard-axis ordering originates from a competing exchange anisotropy as often proposed for other heavy-fermion systems. Instead, it points to an order-by-disorder based mechanism.