How feasible is the production of antimuonic atom? How feasible is the production of antimuonic atom (antimuonic antihydrogen)? It would be interesting to study the 2S-2P transition in this bound state given that the mass of the (anti)muon is greater than the mass of the electron, so that the energy levels are much more sensitive to the finite size of the (anti)proton.
 A: There have been experiments involving muonium-antimuonium, some time ago (1990). 

A search is described for mixing of muonium (μ+e−) and antimuonium (μ−e+). Thermal muonium was produced by stopping muons in a SiO2 powder target. As a conversion signature, a μ− from antimuonium would create Ta184 in an adjacent tungsten foil. The surface layer of the sample was chemically extracted and counted in a low-background germanium spectrometer; no conversion events were observed. The resulting upper limit on the probability that a muonium atom spontaneously converts to antimuonium is 2.1×10−6 (90% confidence). This corresponds to a limit of 0.29GF on the effective four-fermion coupling constant between muonium and antimuonium.

The results are limits, and have not raised an interest for further experimental explorations. There has been theoretical interest , for modifications of the standard model which would predict this ,  as can be seen by searching "antimuonium". 
Muonium spectroscopy is studied because it is easy for a positive muon to capture an negative electron and create the atom. The anti atom would involve generating essentially static positrons, and experimentally difficutl situation to retain, with no advantage, at least at present. No extensions of the standard model expect changes in the electrodynamics of low energies, afaik, and  such an experiment would be a lot of trouble with no reward, as any effects can be studied with muonium atoms.
