Your plot will not be believable unless you provide the set up and motivation for what happens and why your characters act the way they do. Given sufficient set-up and motivation, anything can happen. Absolutely anything.
What you must previously establish in order for your scene to be convincing.
OK. We have a hero who wants a marriage of convenience because he needs money and a heroine who wants a marriage of convenience because she believes it will save her from icky Cousin Fred.
You have to make me, the reader, believe in the motivations. Here's a list of some of the things I'll have to believe in order to buy that this hero and this heroine will enter a marriage of convenience (and, yes, some will be more work than others).
Now, you have to make me, the reader, believe in the motivations. Here's a list of some of the things I'll have to believe in order to buy that this hero and this heroine will enter a marriage of convenience (and, yes, some will be more work than others).
Let's take the first item from the list above: The hero needs money more than love. Here's a list of possible reasons for this to be true:
Let's say it's the first one, threat of foreclosure. Put in other words, the set up for your hero's money motivation is the threat of foreclosure. Therefore! Somewhere in your story before you introduce the solution of a marriage of convenience, you need to say he's about to lose the family home unless he comes up with a chunk of cash. (Ah, but that, too, implies certain things about your hero, namely that a foreclosure is a terrible thing for him.)
Examine your hero's motivations for what he does. Deconstruct his motivations and make sure each element is convincing.
Do the same thing with the rest of your characters.