I use beef broth (Swanson, the one with lower sodium) instead of beer because my husband doesn't like the taste of the beer in it. It's really tasty. You can use chili seasoning packs from the grocery store, but I usually don't because they have too much salt. I use minced garlic, chili powder, ground cumin, oregano, onion powder (I use onions too, so it's to taste), salt and pepper (and sometimes a touch of freshly ground nutmeg... I know... I'm weird, but it's good). You really don't need a recipe without beans. Just leave them out of any recipe you find, lower the seasonings slightly, and expect it to make less food. We also put canned diced tomatoes in ours. One can per pound of beef. I usually thicken mine at the end with flour or cornstarch, but you don't have to. Just experiment with the ingredients, do a few taste tests, and then leave it to simmer on low in the slow cooker. You'll do just fine!
Edit:
I just realized that my "recipe" may have been a little confusing, lol. So... I'll try and sum it up a little bit.
1 lb ground beef
1 can diced tomatoes
1 can (approx 15 oz) beef broth
1/2 of a large onion, diced
Seasonings to taste: minced garlic (or garlic powder if you're desperate), chili powder, ground cumin, oregano, onion powder, salt, pepper
Brown the meat, then move the meat to the slow cooker. I'd also cook the onion in the meat drippings, but you don't have to. Then put everything into the slow cooker and turn it on. You can choose to thicken it at the end with a slurry of flour and water (you'll have to cook it a while longer to get rid of that raw flour taste... blech!) or cornstarch and water (my preference... it's fast), but if you like it thin, then leave it be.
Of course you can easily double, triple, etc. the recipe. Easy! Good luck!