The ATO have released three IDs (interpretative decisions setting out their POV) on this issue:
ATO ID 2010/159 - Deductibility of card payment fee incurred in paying income tax liability under section 8-1 of the ITAA 1997
ATO ID 2010/160 - Deductibility of card payment fee incurred in paying income tax liability under section 25-5 of the ITAA 1997
ATO ID 2010/161 - Deductibility of card payment fee incurred in paying income tax liability under section 25-25 of the ITAA 1997
Each deals with a different section under which you might get a deduction for the CC fees being s8-1, 25-5 and 25-25.
So far they have only ruled on wage and salary earners. These IDs are not legally binding but you can take it that the ATO will administer the Acts on the assumption that they are correct.
When it comes to 8-1 deductibility, sole traders and companies may be in a different position because the ATO view has always been that interest a sole trader or company pays when borrowing to pay tax is deductible under s8-1 as a business expense:
ATO ID 2006/269 - Deductions and Expenses: interest incurred on moneys borrowed by a sole trader to pay income tax
By analogy their CC fees when paying tax may well be deductible under s8-1.
I also note that the ATO say on their website that:
The CPF is deductible to the extent that:
you incurred it as a result of paying an income tax liability and you did not borrow money from your card provider to make the payment
If this is the ATO view an easy way to get within this exception may be to put your card in credit before you make the payment. This exception seems to be based on the view in 2010/160 that the reason you aren't entitled to a s25-5 deduction is that the CC fee is a cost which falls within the exclusion for "expenditure incurred...in borrowing money". If the transaction doesnt include a borrowing that ID seems to say that the CC fee is deductible under 25-5.
DISCLAIMER: This isn't legal or tax advice, just some interesting points put up for discussion.