In the state of Missouri can you get a tax return for your kids and no income.

Not sure about MO, but you cannot get a federal tax return without income --- you will have nothing to enter on a federal tax return if you have not received taxable income.   All of the child-related federal credits are based on income from working.   There has only been one tax year -- 2021 -- for which you could get child-related credit even if you did not work.  The tax laws have changed, and that is no longer the case.

AND….If you have children but had  little or no income, it raises the question of how you and the children were supported.  There may be another tax-paying adult who can claim you and/or the children as dependents.