you can doit by dynamic query.
and convert @doctorid in varchar using convert command.
DECLARE @qry VARCHAR(max)
set @qry ='UPDATE tblDoctorsAvailability SET ' + @Day + '=' + @Timestring + 'WHERE DoctorsId = ' + convert(varchar(10),@DoctorId) +'
print (@qry)
EXEC(@qry)
in place of convert you can also use cast command as
DoctorsId = ' + cast(@DoctorId as varchar(10)) +'