Typically, in these cases, the Businessman would sue the paper, not the woman (if for no other reason than the former has the money, the later does not.).
If the paper says "OP accuses Mr. Businessman of Rape" in it's headline, there is no false statement. The Original Poster did in fact accuse Mr. Businessman of rape. There is no getting around that. As long as the newspaper only refers to the accusation as alleged (the alleged crime, the alleged rapist) there is no false statement, as at this point, Mr. Businessman is accused of a crime.
If you have gone to the police and accused Mr. Businessman of the crime, then Mr. Businessman's defamation suit is meaningless, as it's implied that going to the police implies you believe it happened (no reasonable person assumes you do not believe these accusations you have levied.).
If you say to the press "I believe Mr. Businessman raped me." but do not press charges, that is also not a lie. You can believe whatever you want.
Any accusation made in good faith is not a lie. Any belief of an event happening without evidence that the event occurred is not a lie, it's what you believe.
However, if you say "Mr. Businessman raped me" even though you know he did not and Mr. Businessman can sue you for defamation which will likely impose some court order barring you from spreading that lie in the damages. If this happens, your ability to say "Mr. Businessman raped me" is not something you have to answer for. The burden of proof is on Mr. Businessman. Part of that proof is saying that the charges are false.
However, what you are doing is charging Mr. Businessman with a crime. At that point, the burden of proof is on you to produce evidence to back up your claim. Until Mr. Businessman is accused in a court of law, he is innocent. In effect the suit is forcing your hand and demanding you produce your evidence while Mr. Businessman is refuting your claim.
If Mr. Businessman was someone who would be known to the larger community OR was a celebrity or a politician or otherwise immediately recognizable, then you might have an out, as Mr. Businessman has to prove you have malice in this accusation (P.S. Comments like "OK, so I am fine defaming people so long as there is no way to verify whether the alleged acts happened or not." in comments elsewhere on this thread would make Mr. Businessman's legal team salivate as it could prove malice if found).
However, if Mr. Businessman was not a public individual (i.e. most people wouldn't know who he was until the news reported your accusation) then malice isn't required to prove (or you could say it has been because you put the public spotlight on him by this accusation, immediately giving him a reputation for something he did not do). Famous people have to meet that burden of proof because there are accusations made against them that are not true all the time and not always for actual crimes (Ted Cruz was accused of being the Zodiac Killer during the election (mostly as humor). Despite the fact that Cruz was born over a year after the first Zodiac Killer murder, 10% of Americans believed this statement to be true when polled. Needless to say it could have hurt his election, but it was intended as good clean fun.).
This assumes that you did not file a police complaint. If you had, and they determine you lied to them, you can get some criminal charges filed against you (waiting police time/resources or filing a false complaint... depending on what the statute is called in your jurisdiction.)
If you are bent on ruining Mr. Businessman's life with a false accusation of rape, DO NOT DO IT. For starters, if you lose the defamation case, you have made the wall that much higher for anyone who in good faith makes the accusation, as they will be seen as liars like you. After all, Mr. Businessman could still be raping someone else. It does her no good if you lie, because now his lawyers will use that against his real victim.
If you don't care about potential real victims of Mr. Businessman, consider your own potential safety. If you make a false accusation to ruin someone's life, and then actually have to accuse someone of rape in good faith (God forbid) you have handed that new defendant's lawyer a great tool against you. The defamation trial will come up, and, even if you won that case, it can still be used to prove a pattern of accusing people you don't like of terrible crimes and offering weak proof. You can only cry wolf so many times before the town believes that there is no wolf.
If the story has not gone to print yet, I urge you to retract it ASAP. Better your journalist friend be mad at you than the potential legal nightmare you are about to craft. If it has (and if Mr. Businessman has had you served) better start looking for a lawyer.