Is it possible?
Is it possible to throw a curse on someone without performing a classic ritual? It sure is. Greater Magic, depending on which perspective you take on it, can be with or without ritual. Most Satanists will tell you that a curse cannot work without a ritual. This is because it doesn't work for them, as they believe they need it. Why do they believe this? Because the guru's before them have told them this. Why did the guru's say this? Because they believed it as well.
Be Sure.
Ok, first of all, don't even try to throw a curse on someone that you do not desire extreme harm to come to. You have to want this, and want it bad. If there is any doubt that you want it, then don't even throw it, as it will come back to haunt you. It will not come back in the sense that what you threw will come directly back to you. Instead, it will return as lessened ability to perform magic in the future, and shame at your failure.
Two methods.
There are two methods to make this happen. The first is the absolutely obvious. You must want it to happen. You must will it to happen. While ritual is often helpful for most people, the constant pushing of your will for your opponent's demise can make it occur. It will influence those around you, and those around your target, eventually making their life a living hell. It will unconsciously permeate around you, making your goal come true. However, keep in mind, that keeping up such a strong will for the long periods necessary can be draining. It is stressful to your body. Which can be, at times, counterproductive. It is best that your target is unaware of your intentions.
Using your own will to make it happen is good for some enemies, is often the harder of the two. The other is to have you own enemy will it to themselves! Now, you can imagine, this cannot be done with just anybody. A person who is open to suggestion is the best target for this. Prophecies, it is said, are self-fulfilling because of the people wanting to believe it true. The same is true with curses! With this sort of curse, you must have intense emotional release for the initial portion of the curse. When you tell them of the curse, you must have all of those emotions inside of you about that person released at that one point.
If they are open enough to suggestion, you describing in detail all of the things that will happen to them will happen. How so? The person, so caught up in avoiding the curse, or the end results of it, ends up tripping on unseen obstacles the entire way as they are so distracted by you! Whether or not what you predict will happen to them actually happens or not, doesn't really matter. In the end, they will view it as actually occurring. A self-inflicted hallucination, or paranoia. If the person thinks that they are the target of some gang that wants to mug and beat the person, the fear will show, presenting themselves as prey. Predators will see this fear, and prey upon them, as they know prey when they see it.
Both of these methods can definitely use the help of your physical help as well. For legal reasons, you may want to avoid all possible contact with the individual. Avoiding contact with the person is especially good when performing a curse of the second sort. They believe you are working in the shadows, pursuing their demise. Then again, you just may be doing that!
So the person claiming, "You can't hurt me with a curse, as I am strong in my faith!" is an automatic candidate for the second type. The more they scream and shout that they are unable to be harmed, the more they are just trying to assure themselves, even though they are completely unsure. The most devout are the most susceptible.
Use Ritual Too.
While you certainly can throw a curse on someone without ritual, some need or simply prefer having ritual along with it. You can do this as well, in addition to the aforementioned, if you feel it necessary. Whether or not you feel it necessary will determine whether or not it actually is.