Are you allowed to give sewing lessons in the 9 days?
If not doing so would cause one to incur a financial loss, it is permitted. Best to sew non clothing material or fix old clothing and not sew new clothing.
(It is likewise permitted to weave or sew items that are not clothing, in all cases.)
ראה מג״א תקנא, כג. שו״ת בצה״ח ד, נד. הליכות עולם ב ע׳ קמ. חזו״ע ע׳ רט.