when you doubt something you believe it to be false, as when you suspect something you could be thinking it is true or not. For example in sentence 1 you could say I suspect he can't do the job, meaning the same as doubt he can. In sentence 2 if you were to say, I doubt they're a couple, you mean to say you think they are not.
In sentence 2 if you said 'suspected they are not a couple', it would be like saying 'he doubts they are a couple'
I hope that helps, If that doesn't make sense let me know and I'll try to explain it again.