Can I deduct private dance class tuition for my dependents?

No.  Dance lessons are not deductible.    This is just your own personal expense.

Education expenses for grades K-12 are not deductible on your Federal return, whether for private, public, or home schooling, nor are the expenses for tutoring, after school lessons or after school activities, such as dance lessons, sports, etc.  Some states allow deductions/credits for K-12 education and/or home schooling expenses; if your state has these deductions available, you will be prompted to enter them when you prepare your state return.  (As far as I know, the states that offer any sort of K-12 deductions/credits are Arizona,  Illinois, Indiana, Iowa,Louisiana, Minnesota, and Wisconsin)

No.  Dance class expenses are not deductible on a tax return.