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In a previous paper [{\it J. Phys. A: Math. Theor.} {\bf 40} (2007) 11105],we constructed a class of coherent states for a polynomially deformed $su(2)$algebra. In this paper, we first prepare the discrete representations of thenonlinearly deformed $su(1,1)$ algebra. Then we extend the previous procedureto construct a discrete class of coherent states for a polynomial su(1,1)algebra which contains the Barut-Girardello set and the Perelomov set of theSU(1,1) coherent states as special cases. We also construct coherent states forthe cubic algebra related to the conditionally solvable radial oscillatorproblem.

Coherent states for polynomial su(1,1) algebra and a conditionally solvable system