Ideal coconvergence is a generalization of statistical convergence, introduced by Fast and Steinhaus [\textit{H. Fast}, Colloq. Math. 2, 241--244 (1951; Zbl 0044.33605)] and \textit{I. J. Schoenberg} [Am. Math. Mon. 66, 361--375, 562--563 (1959; Zbl 0089.04002)], having applications in number theory, functional analysis and measure theory, among others. In this paper, the author gives some generalizations and complements of results from his joint papers with Filipów. He works out relationships between ideal equal convergence and various other kinds of ideal convergence (uniform convergence, pointwise convergence, etc.)\ of sequences of real functions. Moreover, he considers an ideal version of the bounding number on sets from coideals. For Part I see [\textit{R. Filipów} and \textit{M. Staniszewski}, Cent. Eur. J. Math. 12, No. 6, 896--910 (2014; Zbl 1315.40004)].