Tony, that is incorrect. 'Convenient' means that it is 'handy' or 'practical' for something to be done or to happen. It is an adjective, not a verb or feeling. You cannot 'feel convenient'. 'A convenient time' means a time that is suitable, practical, appropriate and fitting, all of those at once.
For example, you could say 'the shop is very close to my house, which is very convenient'. You could also say 'the shop is conveniently close to my house'.
Tony, if you read this, your comment that a 'child is conveniently sad when they don't get their toy' is incorrect. Do you mean that the child starts cry at the right time, so that the parents have pity on her and give her her toy? If that is what you mean, then you are right, but convenient just means that it is 'handy' that it happened.