What type of transactions is the stockholder's receivable account used for? Or is there even such an account?

I've never heard of this type of account. You pay stockholder dividends after they are declared by a company. You would be given how much dividends per share to pay or a total amount to pay and the journal entry would be: Debit Retained Earnings for the amount to be paid and Credit Dividends Payable for the amount. When the dividends are paid to shareholders the journal entry will be: Debit Dividends Payable for the amount and Credit Cash for the amount.

Are you sure you mean literally "stockholder's receivable"? I've not heard that name. However, there is a such thing as a receivable from a to-be stockholder dealing with stock subscriptions. If that is what you are doing, then you need one of the people who can do the more advanced corporate stuff. If you have no idea what subscriptions are, then whatever it is you're trying to do likely isn't involving any kind of receivable.