If I try to play a Stadium card but it is discarded by the effect of Chaotic Swell stadium, can I play another one?
No, it was immediately discarded without effect, but you already played a Stadium card which can only be done once per turn.
Source: Cosmic Eclipse FAQ (2019-10-18), TPCi Rules Team (2019-10-31)

Relevant cards

Note: All applicable cards may not be listed below.
SM12_187
SM12_187