Andy,
How I would handle this is to receive the funds and code it to a "current liability" account. Name it what you want. When you write a check to the vendor for those funds, code the check to the same liability account. (which will zero out the liability). You can do this continuously in the same account if it's an ongoing thing, just make sure you reconcile it every month.
This will show up on your Balance Sheet, but that is truly what it is, a liability, meaning you will have to pay it back sometime.
If the payback is more than 12 months, create a long-term liability instead of current.
Let me know if you have any further questions on this.