Several of the above suggestions are good, so I'll play devil's advocate and try to find flaws in the killer's methods.
:
1. Drugs are always good, but did the victim usually use drugs? If not, where did she get them, and when? Is there an empty drug container near the body? It would be tested for fingerprints and DNA.
2. Hanging is a good method, but a good forensics team can probably determine whether the victim was first strangled (e.g. by an electric cord) and then strung up to look like a suicide. The marks on the neck would be different. Also--this is an old one in mystery fiction--if the hyoid bone, a small bone in the neck, is broken, it typically indicates manual strangulation, even if the victim has later been hanged by a rope.
3. Pushing someone off a cliff is good, but how gullible is the victim? Even if I had no great fear of my companion, I'd be reluctant to step closer and closer to the precipice. "Just a little closer, there Nymtoc, so I can get a better picture! Step back a little closer! Closer! Just a little closer!" Whoosh! (But such murders have happened. I recall a real one in which the victim had been slightly drugged before the event, just enough to make her woozy.)
4. I would stay away from knives, since forensics can determine quite accurately how cuts were made, whether by the victim herself or by someone else.
5. Guns are tricky--assuming your characters have access to them. The angle of the shot, how close the muzzle was to the victim, whether there is gunpowder on the victim's hand etc., can all be determined. And, of course, whose gun was it?
6. The suicide note. An old trick in mystery stories is to have someone unknowingly sign a suicide note. This can be done, for example, by asking someone to sign an innocent document, while cleverly slipping the actual suicide note in its place. There's always forgery, but that can be detected, or at least suspected, by experts. I would say that any suicide note without a signature--even in today's hyper-digital world--is suspect.
7. Drowning is good, but the main way people drown themselves is by walking into the surf. The killer would have to make sure there are no, or at least few, marks on the body. He would also have to make sure that the water in the lungs is consistent with the water in the place where the body was found. In real life, people have sometimes been murdered by drowning in a bathtub and then had their body thrown in the surf. The water in their lungs would be fresh, not salt, revealing the crime.
8. Apart from the dramatic push off a cliff, there's always a fall down the stairs. That's a real-life method that has been used fairly often and disguised as an accident. When the murderer is caught in such deaths, it's often because there's too much trauma to the body--all kinds of bruises and cuts, which wouldn't result from a simple fall. Also note that, even if you push your victim down the stairs, he or she won't necessarily die and will survive to point the finger at you.
9. Messing with someone's car. Possible, but today's experts are often able to tell what you did to the vehicle. And who would commit suicide that way? Maybe deliberately driving a car off a cliff or into a tree could disguise a murder as a suicide, but again, experts can figure out a lot by tire tracks, etc.
In conclusion, I think I would choose drugs or hanging, but beware of the caveats above.
I haven't tried these murder methods myself yet
, so I can't guarantee which method would work best.