Increasing the allowances on his W-4 will decrease the amount of tax computed to be withheld. The most is withheld with zero allowances.
But there is nothing you can do to help get more paid in so he does not have a balance due at the end of the year if you are already using all of his salary for taxes. You can not get more than that paid in for him.
He could make estimated income tax payments to have more paid in or he can just know he will owe and save the money to pay by the due date next April.
Federal estimated tax payments are explained at http://www.irs.gov/Businesses/Small-Businesses-&-Self-Employed/Estimated-Taxes
Tennessee tax is only 6% so he likely does have enough paid in.
If needed a payment can be made online. See https://apps.tn.gov/etax/
Please ask if you need more discussion or clarifications.