Can i write off my child care payments to Uncle who does not have a business?

based on the info you provided you may be eligible but you have to file form 2441 with your return to get the credit and you need a qualifying child and qualifying expenses.

WARNING: the IRS compares the 2441 info with the tax returns file by the provider.  

your child or children qualify if one or both children are under 13 and you can claim them as a dependent 

Qualifying expenses

if the care is provided in your home you probably needed to issue your uncle a w-2, file schedule H with your return and likely needed to register with the state and IRS for unemployment and payroll tax purposes. in this situation., the IRS will compare the info on the 2441 to the w-2. failure will cost you because no credit will be allowed and you may not be able to claim the credit for some future years.

if not performed in your home you probably needed to issue your uncle form 1099-NEC if you paid him more than $600 during 2020. he would need to file his own tax return and report this a self-employment income