For some children colouring can be a nice safe relaxing activity and I'd hope that if they wanted to do it a nursery would provide it because if nothing else it supports some of the fine motor skills children need to develop for writing.
It simply doesn't particularly support learning and shouldn't really be feature of an Early Years curriculum.
OP, I think it's fine to encourage children to persist in something they've chosen to do but not if the child was in tears and not if the child didn't even want to start the activity in the first place.
If a child chose to start a colouring activity for a purpose like producing a picture to give to someone and then became worried about it not being good enough I would offer lots of encouragement and support because the child had a target he/she was motivated to achieve and would benefit from completing it.
If I was going to encourage a child to engage in an activity they don't want to do I'd have to be very clear that there was a significant benefit to him/her.
If your son asks to paint and would like you to help him that is great. If the nursery send work home for him and he wants to do it that's great too, although I'm not sure that homework itself is of any benefit at his age.
Please don't think I'm suggesting that you don't participate in joint activities with your son. It is just about the best way for him to learn. I simply wouldn't guide him towards activities he wouldn't choose to do and I certainly wouldn't ask him to do something just because the nursery has sent it home as homework.
Children learn best through playing and following their interests. Going with your son on his voyage of discovery, finding activities which engage and excite him is a much better way to help him to be a confident and persistent learner. This will, eventually, mean he gets far more from school and from homework for years to come. It's also much more fun for us than persuading them to complete a task they are not enjoying 