Not allowed to make purchases from this account

Hey there Bryceb3939!

Have you had a chance to head on over to account.microsoft.com to make sure your billing information is correct and up to date? Let us know

Currently his account doesn't allow him to make purchases. Can I give him gold access and still prevent him from making purchases without my authorisation?

If the purchase is coming from the restricted account(s) then there should be a prompt asking for the password/pass code for the parent account of the child(ren)'s account. (That's how it is on my console.) After entering the password/pass code, you will
be allowed to make purchases on the restricted account for a limited time. Assuming this didn't happen for you, there's another way. You'd have to change the child(ren)'s account permissions, allowing them to make purchases. After the purchases, you may change
the permissions back, restricting the child(ren)'s account once again.

Firstly changing the date of birth on a child account is not going to change it to an adult account on its xbox profile.

if the child account is set so that it can not make purchases the easiest place to go to make that change is account.microsoft.com/family and sign in with the parent account and it should give you the option there to allow purchases by the child account.
then when you are finished making the purchase if you don't want them to be able to make purchases again you would just go back to that same website and choose to not allow them to make purchases

Hey there ENIGMATICSOUL88,

If you are receiving the message "Your account is unable to make this type of purchase on Xbox.com. Please complete this transaction from your Xbox" then this error means that 1) the Microsoft account that you're trying to use to make the purchase doesn't
have the ability to make the purchase 2) Child and teen accounts are prevented from making purchases in the Xbox 360 Marketplace. Changing your Microsoft account age or your purchase settings won't resolve this issue. Make sure that if you are an Adult account,
your account settings allow for Xbox 360 Marketplace purchases. If you are under the age of 18, you will not be able to buy 360 games from the Xbox One. To resolve this issue, purchase or download the content on your Xbox 360 console.

Thanks!

~Blitz