RSA: Private key given public key, plain text, and cipher text with no padding?
No there is not. 

First of all the key size needs to be bigger then the message otherwise RSA will not work

Remember one thing, if you have a public key you can have as many clear texts and cipher texts as you want. This is because everyone can use your public key to cipher a message. So if there was a method were by knowing the public key, clear text and cipher text you could discover the private key RSA would not be used. The question of whether the Padding is used or not is irrelevant. Knowing the public key you can cipher the messages using padding or no padding it is your choice. I am sure that in java you will have providers that implement RSA with no padding so you right now can get millions of clear texts and cipher texts from any public key.

Now why this can't happen:

$C^b = M\ mod\ N$

Being C the ciphertext, b the private key and M the clear text. Then you get

$b = \log_c M\ mod\ N$

And this is the problem. This is discrete log which is in NP. So you can't solve this in polynomial time even if you have infinite number of ciphertexts and clear texts