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From a quick Google search, one can find a table of the first Clebsch-Gordan coefficient. For example this table. Those are used to pass between the tensor product bases and the bases as sum of irreducible of the tensor product of two irreducibles representations of $U(\frak{sl_2})$.

I was wondering if there is such a table somewhere for the quantum Clebsch-Gordan coefficient, that is those occuring when you replace $U(\frak{sl_2})$ with $U_q(\frak{sl_2})$.

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For rank-two quantum groups the Clebsch-Gordan coefficients are tabulated in arXiv:1004.5456 by Ardonne and Slingerland. This also includes mathematica notebooks to perform these and similar calculations.

More tables are in Hegde & Ramadevi.

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