Any decent sized tongue will work here, so use what you can find. A word on peeling them after they've simmered: You need to do this while they are still hot, otherwise the skin will stick to the meat and it'll be a pain to remove later.
You need to simmer the tongues first. You can go as simple as simmering them in beef or chicken broth, or if you want to do water, add some bay leaves or avocado leaves, some chopped onion and maybe a carrot or two. See below for some tips on the making a great simmering broth.
Once the tongue is tender, which will take about 2 to 3 hours, remove it and, as soon as it is barely cool enough to handle, peel the skin off it. You might need a paring knife to help you with this. Discard the skin. Strain the broth and use it for some other purpose later.
While the tongue is simmering, mix the onion with some salt and the lime juice and let it sit at room temperature. This is best done the day you serve, but you can keep the pickled onion in the fridge a day or three without it getting nasty.
When the tongue is ready for the grill, get your fire nice and hot. If you are using smaller tongues, leave them whole. If you are using a large beef or elk tongue, cut it into 3 or 4 large chunks -- this will open up more surface area for browning. Coat the tongue with a little oil and grill until nicely browned.
When you are ready to serve, chop the tongue well and serve with the onions, salsa and cilantro on the tortilla of your choice.