- 2014 American Physical Society. We show theoretically that it is possible to create and manipulate a pair of bound states in the continuum in ultracold atoms by two lasers in the presence of a magnetically tunable Feshbach resonance. These bound states are formed due to coherent superposition of two electronically excited molecular bound states and a quasibound state in the ground-state potential. These superposition states are decoupled from the continuum of two-atom collisional states. Hence, in the absence of other damping processes they are nondecaying. We analyze in detail the physical conditions that can lead to the formation of such states in cold collisions between atoms and discuss the possible experimental signatures of such states. An extremely narrow and asymmetric shape with a distinct minimum of the photoassociative absorption spectrum or the scattering cross section as a function of collision energy will indicate the occurrence of a bound state in the continuum (BIC). We prove that the minimum will occur at the energy at which the BIC is formed. We discuss how a BIC will be useful for efficient the creation of Feshbach molecules and manipulation of cold collisions. Experimental realizations of BIC will pave the way for a new kind of bound-bound spectroscopy in ultracold atoms.