If the cough has stopped then you say "my cough or coughing has stopped"
If the cough or coughing is getting better you can say only one of the two alternative words you mentioned and that is eased.
"my cough/coughing has eased/is easing" these are alternatives to "getting better"
"Slackened is used when tight things become slack. Or to express that someone is being lazy or not doing their share of the work"
"get a move on you are slacking" = you are taking too long wasting time not working fast enough or hard enough.