The easiest way to deal with non-numeric data is to give contour numeric indices into the data and use the data as your TickLabels:
xoptions = {'left','center','right'};
yoptions = {'bottom','middle','top'};
nx = length(xoptions);
ny = length(yoptions);
contourf(1:nx,1:ny,randn(ny,nx))
set(gca,'XTick',1:nx,'XTickLabels',xoptions)
set(gca,'YTick',1:ny,'YTickLabels',yoptions)
Datetimes are similar, but you need to turn them into strings before using them as tick labels:
yoptions = datetime(2015,1:3,1);
ny = length(yoptions);
set(gca,'YTick',1:ny,'YTickLabels',datestr(yoptions))
