Many small liberal arts undergraduate colleges in the US have temporary adjunct positions often or usually filled by new Ph.D.s. These colleges generally focus more attention on teaching than do research universities, and consequently have infrastructure for mentoring and improving teaching. Many have special fellowships whose goal is specifically to mentor young postdocs interested in a teaching career. At my school, these fellowships require teaching only six courses over a three-year appointment, a generous arrangement.
The US National Postdoctoral Association maintains a list of such teaching fellowships, although I am uncertain of its comprehensiveness. One can also find specific school fellowships by web-searching "postdoctoral teaching fellowships in mathematics."
I suspect analogous summer teaching opportunities would be less useful in terms of development, but perhaps(?) easier to secure. There are many summer math programs for high-schools students; teaching at one of these would be quite enjoyable. I can only mention examples (again, in the US) rather than point you to a comprehensive list: Hampshire College Summer Studies in Mathematics, Cornell Summer Math Institute, Berkeley Math Path Summer Camp, Johns Hopkins Center for Talented Youth, etc.