Dimensionality is known to play an important role in many compounds for which ultrathin layers can behave very differently from the bulk. This is especially true for the paramagnetic metal LaNiO3, which can become insulating and magnetic when only a few monolayers thick. We show here that an induced antiferromagnetic order can be stabilized in the [111] direction by interfacial coupling to the insulating ferromagnet LaMnO3, and used to generate interlayer magnetic coupling of a nature that depends on the exact number of LaNiO3 monolayers. For 7-monolayer-thick LaNiO3/LaMnO3 superlattices, negative and positive exchange bias, as well as antiferromagnetic interlayer coupling are observed in different temperature windows. All three behaviours are explained based on the emergence of a (1/4 ,1/4,1/4)-wavevector antiferromagnetic structure in LaNiO3 and the presence of interface asymmetry with LaMnO3. This dimensionality-induced magnetic order can be used to tailor a broad range of magnetic properties in well-designed superlattice-based devices.