You could conceivably talk about time dilation for coordinates built from an accelerator muon frame. For non-inertial motion you can only talk about local
frames in a unique way; then there are many approaches for extending a local frame to coordinate patch. However, typically, it cannot cover much spacetime. So you have a non-unique, quasilocal, coordinate patch in which time dilation takes a complex form [edit: really, the metric takes a complex form; the metric then determines time dilation for a specific path in the coordinates]. Further, in such a coordinate patch, you would typically have features like light and clock paths with coordinate speed greater than c; and your time coordinate would not be everywhere timelike (unless you restrict coverage of your patch even more). Note, this is all SR here - I am not referring to GR at all, just the issues involved in setting up coordinates such that an arbitrary non-inertial world line is the time axis, and coordinate time represents clock time along this world line, and distance coordinates represent proper distance from it according to some reasonable simultaneity convention. Given, especially, the non-uniqueness of all of this, it is rarely useful to talk about an accelerator muon's coordinates (and therefore, about time dilation from the accelerator muon's point of view - that requires such coordinates).
For these reasons, in the accelerator case, we choose to focus on the coordinate independent differential aging rather than the coordinate dependent, complex, time dilation.