Because there have been a few months from the last comment, I want to confirm I was able to make a payment with CC today for my July install that was invoiced today.
My invoice email included a PayPal link, but it was broken, so I called in instead.
I made one partial payment in the morning, initiated a transfer to my credit card to increase my limit, and made a second transaction this afternoon.
For some reason the first came through on my CC as SOLARCITY and the second as TESLA MOTORS INC.
The only difference was that the first time I had a 'get a callback' option and the second time I was on hold until someone picked up. I'm guessing that means they have different support teams with varying internal systems. The tech making the second transaction (that came through as TESLA) mentioned he was in Utah, in case anyone wants breadcrumbs to try to figure out how to get it to come across TESLA (for example if a credit card treats them differently)
Both transactions are currently pending, and when I asked he mentioned they should clear within 3-5 business days.