You could do something likeget the date for next Sunday, add N days and print the day name for that particular date:
getdayname () {
date -d "$(( $nextplus=$(date -d "$(( 7-$(date '+%u') ))"next days"Sunday '+%u')+$1 )days")
date days"-d "${nextplus}" '+%A'
}
and run getdayname 2, getdayname 7 etc (assuming gnu date).
Or simply use an array and do without the date e.g.
getdayname () {
local days=( Sunday Monday Tuesday Wednesday Thursday Friday Saturday )
printf %s\\n ${days[$1]}
}
though with bash/ksh you need printf %s\\n "${days[$1-1]}" (as indexing starts at 0), and quotes are needed to avoid split+glob (also with yash).