Since he has paid nothing, you cannot really buy him out, except for a nominal sum. I understand you do not want to get the Court involved, but try telling your partner that if he does not accept whatever sum you offer, you will sue him for specific performance of the partnership agreement an then he will have to contribute his share.
Since I do not know what your partnership agreement provides, I cannot tell you specifically which, if any, provisions you can rely on to dissolve the partnership; but I can say this, go over every paragraph of the partnership agreement and see if there is any provision that applies to a partner's failure to perform his obligations under the partnership agreement.
If he still will not budge, look for the provision in your partnership agreement which allows for dissolution of the partnership. If no provision for the dissolution was made in the partnership agreement, you may have to go to Court to have the partnership dissolved by the Court.
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ANDREA, JD, LL.M., Taxation
Member, NY & PA Bar
DISCLAIMER: The facts stated herein are information only and are not intended, nor should be construed as legal advice or legal opinion and No Attorney-Client relationship is formed by asking questions and receiving information; laws vary from state to state and to protect your interests, you should seek local counsel