I have no burden to prove a negative. You positively affirm empiricism so it is your burden to prove it.
Actually, you do have a burden of proof. Attempting to deny it accomplishes nothing and appears to be both dishonest and hypocritical. The problem is that you have in no way fulfilled that burden of proof. Logical proofs (such as the [wiki]coherence theory of truth[/wiki]) do not suffice, because you can prove things using logic which are demonstrably not true. For example, Zeno's halfway paradox can be logically proven (even though it is demonstrably not true). Because of this, you cannot rely on logic as your proof; it results in paradoxes that are impossible to resolve using logic.
This is the fundamental problem with your reliance on the coherence theory of truth. Attempting to verify a logical proposition (as coherence theory is) with logic is meaningless, because the premise of a logical proposition can be false, yet the proposition itself can be true. While you can write a logical proposition that results in that premise, said logical proposition itself has a premise. So you either end up with circular logic or "turtles all the way down". Furthermore, neither can deal with the essential problem of being able to test the actual validity of the original premise to begin with.
That's where empiricism usually comes in. Yet you've asserted that empiricism itself is invalid, so you cannot use it. Therefore, you have nothing to check the premises of your logic against. Your only option is to attempt to use logic to verify those premises, but as I have already stated, that simply does not work. It results in either circular logic or an infinite series of logical propositions, both of which are fallacies.
Going back to empiricism, it's true that there's no way to absolutely verify it. But trying to reject it completely because of that is illogical. That rejection relies on a logical proposition, but because you cannot use logic to prove logic, it's impossible to disprove empiricism without using empiricism. So, it's impossible to conclusively prove that empiricism is valid, and it's impossible to conclusively prove that empiricism is invalid. What does that leave us with? Whether empiricism is useful. Unlike trying to prove that it is (or isn't) valid, which is not relevant since it's impossible either way, you can show that the results of empiricism are useful.