This is so tough.
I have had an associate take over the negotiation process of one. How can you advice one to go up in price or change terms and void all knowledge of the other buyer's offer. Sometime you get lucky and one buyer just can't compete.
Once negotiations are complete, I resume all responsibility back for the buyer who has been awarded the home.
This happened to one of my colleagues in my office last year, and she had me write up and present the offer for one of them while she presented the other. Once the deal was negotiated (my client got the house), she took over most of the chores from there (I did attend the appraisal) and paid me a referral fee for handling the negotiations.
You could also have your broker handle one of the offers.
As a Buyer Agent you have a responsibility to protect the interests each of your clients. Even if you have one or more clients bidding on the same property, the details of the offers must remain confidential. Counsel each one by providing your usual, objective and professional representation.