The easiest way to do what you are looking to do would be to set up your son's account as a Child Account under your own account. This would allow the use of a credit card linked to your account to purchase apps, or install purchased apps, on his account.
It will also, for security reasons, require your Windows Account ID and Password in order to purchase apps with the credit card.
I realize this information references Games for Windows Live but since it's all dealing with Windows Live Child Accounts, and it was the most informative article I could locate, it should still be relevant. Also bear in mind that Xbox Live, Games for Windows
Live and all other Microsoft Account related services will use the Windows Live ID, or "Microsoft Account" as they're now referred to.
The information below is from this website.
To create a Windows LIVE ID account for a child (minor), you must provide a Windows Live email address that you can designate as a Parent account. If you do not already have a Windows Live email account, you must create one before you can create a Child
account.
After the Parent-to-Child account relationship is confirmed, you can connect to Games for Windows – LIVE by using the Child account.

After you provide the Windows Live email address for the Parent account, you receive a confirmation email message. You must click the link in that message to confirm your address. This confirmation creates the link between the Parent and Child accounts.
Provide the Windows Live email address for the Parent account, and then click I Accept.

To complete the process, enter the required information on the Parent Age Verification screen, and then click
Create.
Note A Credit Card Verification (CCV) number must be provided in the Security code box as confirmation of age. You will not be charged a fee to sign up. This information is used only to verify the age of the Parent account holder.

You can now log on to the Games for Windows – LIVE website by using the Child account.