Yeah it can work with one coin. It may take more than one flip if all the teams pick the same to eliminate to two teams. Just have the teams select again until there will be two on one side and one on the other side.
Or take a die and have the three teams select two numbers from the six sides and roll the die to determine the top team, then the other two teams select three numbers and roll the die a second time to determine who ends up in the 2nd draft position.

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