With the help of everybody's comments and examples, I think the difference relates to the degree of "control" the speaker wishes to convey. In this case does the speaker wish to emphasise the woman's ability to find a boyfriend or the other factors that are also involved? (eg "money can't buy love"):
The use of 作る to emphasise the subject's active influence is consistent with the above examples:
"I have to find a bf too!"
She flirted with guys in clubs to get a boyfriend
出来る (which has to be used with ように not ために）conveys the importance of other factors beyond the person's control that can determine the final result (such as mutual interest from the intended partner). You could apply the same principle to:
She is pregnant.
"I don't want to have a child before I'm thirty."
Most dictionaries assign a large number of uses/meanings to both verbs. In the Apple dictionary: あの二人は出来ているらしい is translated as "They seem to be in love with each other" or " They seem to be on intimate terms with each other" (emphasizing a physical relationship). 男を作る is defined as "become involved with a man/ have [take] a lover" but having the same meaning as 友達を作る, "to make friends".
出来る is also assigned the more general meaning of "come in to existence" (生じる／生まれる in the Apple dictionary) which emphasises a change of state. It is also close to its use to say the equivalent of "He(A boyfriend) came into her life", or "I was able to find a boyfriend" in the same way that 英語ができる means "I can speak English": in both cases the verbs "find" and "speak" can be inferred.