Criminal cases aren't like civil lawsuits for money. With the latter, the parties have more control over the proceedings. The would-be plaintiff can agree to dismiss or not file suit in return for a specified sum (and perhaps the performance of certain conditions). But in criminal court, the plaintiff is the government, and it isn't seeking money, but rather some variety of justice. So, defendants can't simply pay their way out of criminal prosecution.
There are, however, situations in which the prosecution may agree to drop or hold off on filing charges. (For an example regarding low-level offenses, see Can criminal cases be resolved without going to court?) And despite the general prohibition against settling criminal charges for monetary consideration, in many states, defendants can resolve certain misdemeanor charges through financial settlement with the victim. (To learn more, see Civil Compromise for a Criminal Offense.)
Although there are many ways—including (but not limited to) diversion programs, mental health and drug courts, and expungement and record-sealing opportunities—to avoid or minimize the effects of a criminal conviction, only a knowledgeable criminal defense attorney can properly evaluate whether they apply to your situation. Make sure to consult a lawyer versed in local court practices if you want to pursue any of them.