The only direction in which I can hang a couple nest boxes appears to be south-facing.

One would be under an overhang so not in full sun, and one would be on a confer which has no lower branches so may get a ton of sun.

I know normally nest boxes should face east. Is it better not to hang them when the only available space is south?

I don't think so Jai. I think you will be fine. I think sometimes we humans make to much to-do over pickety little things. I look at it this way ~~~ hang the nest boxes; the birds know if they should nest in them or not. They know better than we.
All my nest boxes face south. The bluebirds don't care & both boxes get a lot of sun. We have fledglings in abundance every year.

I have noticed our east facing boxes have nests in them but I have one box that is south facing and so far no nests.

I have them on all but the north side (between 2 three floor bldgs) here. While I just started here last summer. All are being used/explored. Additionally, my brick house is 128 years old and in dire need of tuck pointing. I say this because I have watched solitary bees exploring all the nooks and crannies for the last two years. They do this on all levels, on all sides, all the way up to the roofline. So they do not seem to have much in the way of limits. I will continue to plant all areas and add enhancements for pollinators on all sides/orientations. I do have some brush, wood, and soil areas on the north side that are cobductive to twig, log, and soil nesters. I am currently trying to figure out how and where to install a sand pit for sand nesters.