I use whole doves for this, as they pluck so easily. If you don't have whole doves, it will still work but won't be as pretty. And for you non-hunters out there, use either squab or quail. The sauce can be refrigerated for several weeks beforehand.
Heat the lard or oil in a medium, heavy pot over medium-high heat and add the grated onion. Cook this, stirring often, until the onion just barely begins to brown. Add the chiltepin or other chiles and then the tequila or mescal, the prickly pear juice, a little salt and the agave syrup, if using. If you are using prickly pear syrup, follow this sequence: Add the chiles, then the tequila and let this boil down by half. Then add the prickly pear syrup and a little salt.
Turn the heat to low and let this simmer until the flavors meld, about 15 to 20 minutes. Add lime juice to taste, then buzz the sauce in a blender to puree the onion. Taste the sauce for salt and seasonings, then put it back on the stove and let it cook down to a glaze.
Get your grill blazing hot. Arrange the doves, breast side up, on the grill and paint the doves with the sauce. Cook for 3 to 5 minutes with the grill lid open. Turn them on their sides and paint them again. Grill for a minute or two, just to get some caramelization on the skin and sauce. Flip and do the same with the other side. Finally, grill the doves on the breast side for 1 minute, just to brown. Take them off the grill, paint them one more time with the sauce and serve.
The sauce does require some esoteric ingredients, like prickly pears and chiltepin chiles. You can substitute other hot chiles if you want, and prickly pear syrup is easy to make or you can buy it online -- there is no substitute for it, as it is the backbone of this sauce.