I am afraid that there are no solution that fits all need. All have drawbacks and advantages.
Accents, if you can do them, work great. Pick a real life language and use an outrageous accent of the same for your Blurbnish. Clearly, the more outlandish and caricature the accent, the better as long as it fits the tone of the game. If the game is real life, then use the real life accent. Another related note is to use words in a real life language within the sentence but that gets complex and unclear quickly.
While some real life accents may be seen as or are racist and offensive, I shall leave it to you and your group to work out one that is not. Follow Wheaton's rule: don't be a dick. If this is really a problem for you, why not invent an accent?
A potential problem with accents, as SevenSidedDie pointed in a comment, is that no one can have accents while speaking a foreign language without being confusing.
Another language, if you both speak a different language, you can use that. Of course, it requires you to be fluent in more than one language. Maybe even use something like Pig Latin.
A prop, like a hand gesture, cards, or a hat. Hats got quite silly so we stopped using them fairly quickly but your mileage might vary. You could use cards or other visual cues but then you have to remember to swap them out and it could get messy with lots of languages. Hand gestures mean that the other players must see you which can lead to confusion if they do not or just miss the cue.
Another prop that might be useful is a small set of flags those country uses the language. This works for real and imaginary worlds but might make your gaming table look like an unholy meeting of the UN...
Just to stop the downvote faerie: Yes, I used all of those in games before. Yes, they worked great. No, no one was offended at my outrageous French accent or at my attempts at butchering English or my silly hat.