Is there a set of standard abbreviations for the days of the week for use in astronomy? I couldn't find any reference to it in the The IAU Style Manual (1989).
Wikipedia uses: mon, tue, wed, thu, sat, sun.
ISO 8601 defines an exchange standard for dates based on weeks and days, which looks like this: 2017-W01-3 or this 2017W011 (Year, ISO week number, number of day of week starting with Monday). Not so surprisingly it does not standardize names of days as far as I can tell.
So you could claim to use ISO-8601 conventions and simply use 1-7 (starting with Monday).
A comprehensive listing of abbreviations of day names for European countries is given by the European Medicines Agency for blistered drugs for the curious.
comments converted to community wiki
The day of the week by itself has no use in astronomy unless you also know the corresponding calendar date. And since the day of the week is computable from the calendar date, it's really just superfluous information. Nevertheless, most astronomy apps such as Sky Safari seem to use the first three letters (in English) abbreviating the names for the days of the week. This use seems to conform with the ISO week date standard.