The first one is correct. Rule: Never follow a preposition with the infinitive, only a gerund.

The first one makes sense. You were in a romantic relationship and she left because you didn't make her laugh enough, and you are taking the blame. The second one doesn't make sense at all. Using the verb, say, "for not being able to make you laugh" but this doesn't work with "my fault for" very well. Most people wouldn't say my fault about being something, but rather doing something.

The first sentence is grammatical but Amy is correct that it would be an odd thing to say. But if you really did something wrong that didn't make someone laugh, you could say that. We just don't see why someone would ever say that. :-) The second sentence is not grammatical. Some examples that would make sense to an English speaker would be "It was my fault for not making you happy." or "It was my fault for making you angry" or "It was my fault for making you late to your meeting."

Sorry, not natural. I don't know what either sentence means. Not being able to make someone laugh isn't a person's "fault". When something is your fault, that usually means you're guilty of doing something that has a negative impact on someone else. An example of that would be something like "It's your fault the milk went bad because you left it on the counter all day. Now I can't make breakfast." or "It was my fault the rent was late because I procrastinated mailing it to the landlord." So the 2 sentences you provided really don't make sense to me.