Summary: Functional magnetic resonance imaging (fMRI) techniques involve studying the brain activity of an experimental subject in response to a mental stimulus, such as a picture or a video shown to the subject. The design problem in fMRI studies is to come up with the best sequence of stimuli to be shown to subjects which enables the precise estimation of the brain activity. In previous analytical studies concerning fMRI designs, it has been assumed that the errors are independent over time. The current state-of-the-art method to find optimal designs for the situations when the errors are correlated is to use the genetic algorithm. In this paper, we analytically obtain the optimal designs in a subclass for the situations when the errors over time are assumed to have an auto-regressive (AR) structure. Since such optimal designs might not exist, in practice, we advocate the use of what we call \(g\)-lag orthogonal designs. We show that these \(g\)-lag orthogonal designs perform reasonably well under a wide range of conditions under the models with correlated errors.