As a sole proprietor, the tax liability of your business is calculated based on combining your business income with your personal income together.
It is good advice to keep all personal and business financial matters separate. This makes it easier to prove to the IRS that all your business expenses are actually business related. In this case however, the two items [tax payment for personal income vs tax payment for business income] are inseparable.
What you can do, however, for your own personal records, is calculate how much of your tax payment relates to your business. I wouldn't get complicated about this; I would simply take the net income of your business as a % of your taxable income, and multiply that against your tax payment. ie: if your business net income is $10,000, and your total taxable income is $50,000, and you paid $6,000 in taxes, I would record that 20% of the $6k was related to business income. If you have a separate bank account for your sole proprietorship, you could make a transfer to your personal account of $1,200, and then make the $6k payment from your personal account.
Remember that tax payments for either your sole proprietorship and your personal income will be treated the same: federal tax payments are not tax deductible, and state tax payments are tax deductible, whether they were paid for your sole proprietorship or the rest of your personal income. So even though this method is simplistic [for example, it doesn't factor in that different investment income types earned personally will have a lower rate than your sole proprietorship income], any difference wouldn't have an impact on any future tax liability. This would only be for your own personal record keeping.