Machine Learning algorhtm that can be trained to learn Pig-Latin
Look at Neural Machine Translation models, you could either 'cheat' and tokenize both the English and the Pig-Latin words or you could make it character based which I think is more interesting and it allows to generalize for words out of dictionary. These models are called sequence to sequence models and there are plenty of implementations that can take pairs of sequences to translate. I think this task can be solved with accuracy close to 100%.

Here is an implementation in Keras: https://github.com/farizrahman4u/seq2seq

Here is an official TensorFlow tutorial: https://github.com/tensorflow/nmt