A number of different methods have been developed for random and directed mutagenesis in actinobacteria (most notably for Streptomyces coelicolor). Many involve an initial mutagenesis step performed in Escherichia coli, with subsequent transfer of the mutant allele(s) into the desired strain i.e. by protoplast transformation or intergeneric conjugation into Streptomyces. Others, such as CRISPR/Cas- or meganuclease I-SceI- mediated genome editing, can be performed directly in the actinobacterial strain of interest.
Your choice of mutagenesis method will depend largely on your intended use, and on whether you have an appropriate genetic screen/selection that you can use to identify your mutant(s) of interest.