The reverse in meaning of 'Don't get your hopes up' is actually 'Be positive !" 'Stay hopeful' is possible if you wish to use the word 'hope', but not as natural as 'Be/stay positive'. You cannot say 'Get your hope up (or down)'.

Thank you! Ellen and Matt. It is very helpful.

Hi Ethan. There is a common phrase: "Don't get your hopes up." But you are correct, that is pessimistic, expecting disappointment. There really isn't a single uplifting phrase that is truly the positive version. You could use: "Don't let [situation] get you down." I used to hang a poster in my classroom my kids would point to it when anyone was upset because they didn't do as well as they hoped. It said: "Be patient with yourself. Nothing in nature blooms all year." Depending on the circumstance, it might help. :) Ellen

it's only used as a negative you haven't been a good boy this year. Don't get your hopes up about any Christmas presents