"Can you show me where the watermelon is?"
Literal translation would be: 수박이 어디(에) 있는지 보여줄 수 있어요?
As for grammar on your trial sentences:
- 어디 수박을 있어요?
- 을 is wrong. 있다 means "to be/exist", so it cannot take an object (and the attendant case marker 을/를) any more than it can in English.
- 어디 수박을 있는을 보여 주세여? (여 -> 요)
- 있는을 is wrong. 있는 is a modifier form used before a noun. You cannot add a particle to it directly.
There are specific clause making verb ending forms like -는지 for such constructions (it may look like adding a particle 지 to 있는 but technically it is a different verb ending form -는지 attaching to the verb stem 있).
- correct sentence: 수박이 어디 있는지 보여 주세요 (-는지 creates the noun clause working as an object of 보여. Also, it is more natural to put the subject 수박 before the adverb 어디(에)).
Going beyond grammar into how natural it sounds, even "수박이 어디(에) 있는지 보여줄 수 있어요?" doesn't sound the best in my opinion. It sounds too fussy for what it's saying.
It is partly because 보이다 and 보여 주다 are used much less in the sense of showing people around a place. In most cases it means physically showing something in front of you. There are other verbs like 가르쳐/알려 주세요 (inform me) or 말해 주세요 (tell me), but all these words sound a bit redundant because the store context (I assume) makes the point so obvious (you want to know their location).
So what do we say then? We would most commonly just say 수박(은) 어디 있어요? or 수박(은) 어디 있죠? (Where are the watermelons?). This makes it clear you want a simple direction so you can go check the watermelons yourself, whereas 보여 주세요 sounds like you want the store person to take you there or even to take one out in front of you. 보여 주세요 would be the right phrase though if you're asking them to show you a particular item, like a certain type of jacket in a clothing store, for example.
In short, I think it sounds strange mainly because 보여 주다 is not commonly used for "directions" as "show" is in English.