Is there an analogue of the Hive model for Littlewood-Richardson coefficients of types $B$, $C$ and $D$?

If $V_\lambda$, $V_\mu$ and $V_\nu$ are irreducible representations of $GL_n$, the Littlewood-Richardson coefficient $c_{\lambda\mu}^\nu$ denotes the multiplicity of $V_\nu$ in the direct sum decomposition of the tensor product of $V_\lambda$ and $V_\nu$. Knutson and Tao proposed a Hive model" for Littlewood-Richardson coefficients in http://www.ams.org/journals/jams/1999-12-04/S0894-0347-99-00299-4/S0894-0347-99-00299-4.pdf

Is there an analogous model for such tensor product multiplicities for Lie groups of types B, C or D?

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The recent work of Goncharov-Shen gives a good generalization of the hive model for any reductive group $G$. They show that $n$-fold tensor product multiplicities for $G$ are counted by positive tropical integral points of the space $G^\vee \setminus ( G^\vee / N)^n$. When $G = GL_m$ and $n = 3$, this gives the Hive model. When $G = GL_m$ and $n = 4$, this gives the octahedron recurrence.
Unfortunately, outside of type $A$, it is hard to give a simple description of their set of positive tropical points. To do so requires some choices, and once one makes these choices, you end up with one of the Berenstein-Zelevinsky models which Allen mentioned.