There are a ton of cocktails that mix tequila and coffee. There are three options for the coffee part of it: canned/bottled, liquor/liqueur, and home brewed/coffee house. Home brewed coffee is fun for experimentation and there are a lot of variables to work with. Coffee has three different growing regions, different roasts, and brewing methods. These things matter very much and make it hard to balance for a cocktail. Keep this in mind when you have a terrible cocktail with home-brewed coffee in it, a different coffee may turn it into something wonderful. Honestly though, most people can't make a good cup of coffee as it is. If you do make a hot coffee destined for a cold cocktail, let it cool first to reduce dilution from the ice. In practice, the same challenges of using home brewed coffee apply to coffee that you get from a coffee shop.
Here are a few that use home brewed coffee:
South of No North: tequila, coffee, cynar, simple syrup, egg white. I have not had this one, but of the cocktails here it's the one I'm most interested in. Cynar is an amaro, a bitter liqueur, made with artichoke. If you've never had an amaro, I would try a few at the bar before buying a bottle. A lot of people don't like them the first time around, ease into it with maybe Amaro Meletti and club soda.
Jalisco Martini: tequila, espresso, and coffee liquor. This is simplest of them all, most in line with what you're looking for. A single shot of espresso should be about one ounce, which is what's called for here. If there is a good coffee house around, I would order an espresso to go and take it home to mix. This recipe was adapted from a recipe by two of the founders of Altos tequila. Feel free to swap Altos, or any tequila, for the Patron which is called for. Patron supports the site author. You can also swap in Kahlua for the coffee liquor for something a little sweeter.
But First, Coffee: tequila, espresso, coffee liqueur, and a spiced coca-cola reduction. This is a sponsored post by a coffee liqueur brand, but it's a good brand. Also, I really like coffee and coke mixed together so this is my kind of thing.
Spiked Horchata: tequila, espresso, Kahlua, almond milk, and agave syrup. From the Kahlua website. Generally, if it's called for Kahlua is not interchangeable with other coffee liquors as it has rum and vanilla that make it unique. The recipe calls for "Olmeca". We can assume "Olmeca" is Altos tequila, probably blanco or reposado. Olmeca Altos tequila is owned by the same parent company as Kahlua, which is the only reason they call for it so, swap it out at will.
Canned or bottled coffees are a little easier to work with than homemade coffee. It's more consistent and easier to swap out. There are a ton of options to choose from though so, when a specific brand isn't called for, there's still some experimentation involved.
Coffee Margarita: tequila, cold brew, Kahlua, lime juice. This sounds... horrifying. It's from the Kahlua website. I'd only give it a try if I already had the ingredients on hand, and I wanted a good laugh. But it could be good, I've never tried it so what do I know?
Mixing coffee drinks is at its most straightforward when they only call for coffee liquors/liqueurs. There are fewer brands to choose from, you'll find a specific brand called for or you'll have a personal favorite. A lot of brands are interchangeable, though some are higher quality than others.
IMO: mezcal, shochu, coffee liquor. Mezcal is related to tequila, like the relationship between Scotch and whisky. Tequila is regulated, it can only be made with blue agave and can only be made in a handful of regions. Mezcal can be made from any number of agave varietals. Shochu is a japanese liquor, in this case made from sweet potato. This is different than what you're looking for, very little coffee here. I include it because this is a super interesting cocktail.
Hot Tamale: tequila, Kahlua, hot sauce. If you thought it couldn't get worse than dumping a bunch of lime juice into your coffee, you can dump a bunch of hot sauce into your coffee. The only coffee here is from the Kahlua, which has very little caffeine in it. There are still other tequila and Kahlua drinks are their website, which I mention for anyone just looking for that coffee & tequila flavor.