Ultrafast electron diffraction enables the study of molecular structural dynamics with atomic resolution at subpicosecond timescales, with applications in solid-state physics and rational drug design. Progress with ultrafast electron diffraction has been constrained by the limited transverse coherence of high-current electron sources. Photoionization of laser-cooled atoms can produce electrons of intrinsically high coherence, but has been too slow for ultrafast electron diffraction. Ionization with femtosecond lasers should in principle reduce the electron pulse duration, but the high bandwidth inherent to short laser pulses is expected to destroy the transverse coherence. Here we demonstrate that a two-colour process with femtosecond excitation followed by nanosecond photoionization can produce picosecond electron bunches with high transverse coherence. Ultimately, the unique combination of ultrafast ionization, high coherence and three-dimensional bunch shaping capabilities of cold atom electron sources have the potential for realising the brightness and coherence requirements for single-shot electron diffraction from crystalline biological samples.