Stay calm, I know it's easier said than done, if you are panicking, it will give your parents bigger reason to suspect that it is wrong. You can't change their opinion though, I have never personally been caught but I think it would work better than if you were stammering, try to rehearse what you are saying and recommend some websites and don't forget to mention that you are not the only one like yourself.
Also be honest and don't lie or that will give your parents even bigger reason to not trust you. Just tell the truth and nothing but the truth, don't beat around the bush or miss things out because they will find out sooner or later or perhaps never if you are lucky! If the diapers are medical or things like "tena" then say you have been having issues and you have accepted it and don't like the idea or going to the doctors, clearly state that you do NOT want to go, you should be 18 plus by now which means that you are an adult and can look after yourself by law and that your parents shouldn't really interfere but of course they proberly will, so be careful if you decide to go down this route,
Alternatively you could tell them if you have AB or actual baby diapers, that you like to be a baby or toddler and you feel this way inside, explain that again you are not the only person who likes baby things and that this won't go away, tell them that you are mentally ill and do not need to go to the doctor or "shrink", if they do send you to see the "shrink" explain to both the doctor and parents that you feel this way and that you know what you are doing and that you are not hurting anybody, exploiting yourself or sexually harassing kids or adults for that matter! Tell them you can balance your life and that you enjoy this when you have free time and won't let this get out of hand. Try to offer them a few sites that accuratly Patray a Little Or adult Baby, don't Show gimiky Shows like my Strange Addiction and Taboo first hand or you Will give them idea that it is something bad and shows like that exagerate!
My best response would be the second one if you are a Little Or adult baby because it's honest and straight to the point and they won't be any more secrets. I can't guarantee that I can make this any easier for yourself as I can't imagine what your parents reactions are going to be as I don't know your parents, I would expect a bit of shouting or your parents being in a huff, but don't be suprised if they accept it totally and even help out by cuddling you or playing with your toys or something or at least talking about it in a positive way. Lastly I would tell them "mom, dad I love you and I hope you finding my diapers and various other things doesn't effect our relationship in any way, I really enjoy our relationship as it is really special to me and I would hate to ruin it just because of a few stuff that may be out of the ordinary to find in my bedroom, this won't effect my life negatively as it has improved my life and wellbeing, I am more happier and less anxious with my diapers, pacifiers and toys, so please consider it or at least sleep on it and we can talk tomorrow when you have had time to calm down and think about it"
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Edit, I typo occurred in the 3rd paragraph, the sentence should be "tell them that you are not mentally ill and do not need to see a "shrink"" blablabla...