I have added Criminal Defense to your categories which is where this question is more appropriately directed. Good luck.
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You face an uphill battle. As always, talking with an attorney about exactly what happened is your best bet, but here are some general thoughts.
First, you may face a time bar -- you must file a notice of appeal soon after your plea is entered.
Second, most plea bargains include a waiver of your right to appeal -- that is, you agreed not to appeal as part of the deal. You would be very, very unlikely to overcome that waiver and appeal. You also probably told the court that the plea was not a result of coercion (even if your son felt coerced, he probably signed something that said he was not coerced). It is very, very difficult to overcome that statement on appeal.
If you missed the deadline to appeal, the other possible option is what is called a collateral attack on the conviction -- a habeas corpus petition. Your burden in these proceedings, again, is very high. This is a very complex area of law and you would want to hire an attorney to help you.
Unfortunately, there are a lot of unanswered questions in your query. Has your son been sentenced? If so, how long since he was sentenced? If he hasn't been sentenced, then a motion to withdraw his plea can be made if there are sufficient grounds, although they are rarely successful. Instead of hiring a private investigator, find a good criminal defense attorney and ask for an initial consultation. Most attorneys offer a free consultation or charge a minimal amount. By the way, when you say there is no force, it sounds like a sexual assault case. Whatever the case, do not discuss facts and details of the case on this site or any internet site because DA's can access this site too and may use the information they get against your son at some future date.