Sequence design is a crucial step in the process of designing or engineering proteins. Traditionally, physics-based methods have been used to solve for optimal sequences, with the main disadvantages being that they are computationally intensive for the end user. Deep learning-based methods offer an attractive alternative, outperforming physics-based methods at a significantly lower computational cost. In this paper, we explore the application of Convolutional Neural Networks (CNNs) for sequence design. We describe the development and benchmarking of a range of networks, as well as reimplementations of previously described CNNs. We demonstrate the flexibility of representing proteins in a three-dimensional voxel grid by encoding additional design constraints into the input data. Finally, we describe TIMED-Design, a web application and command line tool for exploring and applying the models described in this paper. The user interface will be available at the URL: https://pragmaticproteindesign.bio.ed.ac.uk/timed. The source code for TIMED-Design is available at https://github.com/wells-wood-research/timed-design.