There is nothing intrinsically untameable about the Riders, unlike the Wizard of Yendor or Demogorgon, neither of whom can be tamed under any circumstances. (See my spoiler on tame monsters for a complete list of untameable monsters.) However, they are very difficult to tame because they are level 30 and have 100% magic resistance. This means that they will resist any attempt to tame them with a scroll of taming, spell of charm monster or magic harp, or with the revivification technique available to high-level Healers in Slash'EM. The ``You feel charismatic!'' effect of a magic trap ignores the target's magic resistance, but sadly there are no magic traps on the Astral Plane.
Famine and Pestilence can be tamed by draining some levels from them and then repeatedly casting charm monster. Slash'EM Healers can employ the somewhat easier approach of level-draining them until the charm monster spell would have a non-zero chance of working (one level drain is enough if you're level 30), then killing them and resurrecting them with the revivification technique. Death is immune to level drain, and hence cannot be tamed in this way. In Slash'EM, it used to be trivial for a Healer to tame all three Riders by reviving them, but this was considered a bug and has now been fixed.
If the Riders are polymorphed, they will lose their 100% magic resistance and potentially become tameable. They will always resist the wand, potion or spell of polymorph, but if you polymorph into a green slime, you can slime them. This approach is not particularly useful, as all you will get is a tame green slime which was once Death, and since monster polymorph is always permanent in vanilla Nethack, there is no way to tame Death. In Slash'EM, however, you can polymorph into a genetic engineer and hit Death causing her to "undergo a freakish metamorphosis". This is a temporary polymorph, and if you tame Death while she is polymorphed she will remain tame when she reverts.
The answer to this question is highly dependent on the version of Nethack you are playing (or, if you are playing Slash'EM, the version of Nethack it is based on).
There are two factors which must be kept under control when attempting this challenge: hit points and nutrition. If either of those becomes too low, you die. Of course, there are ways to die that don't involve running out of hit points or nutrition, but these are relatively easy to avoid and prove that you are avoiding.
Since there is no way to generate an infinite supply of healing potions, the only practical strategy for keeping your hit points up is to ensure that nothing can reduce them. The psychic blasts of (master) mind flayers can only be defended against by genociding them.
You also have to protect yourself against both melee attacks and ranged attacks. One way to do this is to reverse genocide blue jellies (or some other sessile monster), so that you are surrounded by eight of them, and then read a scroll of earth, so that there are also eight boulders on the squares surrounding you. You may need to repeat this procedure if some of the jellies are killed when you read the scroll of earth. Monsters can't see you through the wall of boulders, so won't attack you from afar, and even monsters that could dig, phase, or pick up the boulders won't be able to get next to you while the jellies are there. Aaron Ranta has done this in wizard mode in version 3.3.1, and has placed a snapshot of his game on the Web.
Now that you cannot gain the unchanging intrinsic, it is difficult to eliminate the need to eat. Wearing the amulet is not sufficient, because it will cause you to consume food at the rate of one nutrition point per 20 turns. Relying on eating monster corpses works wonderfully in a real game, but not in this theoretical discussion. For one thing, perhaps no monsters will be generated for a very long time. For another, when you live on monster corpses you have to kill the monsters and take the risk of them killing you.
There is a tedious strategy involving wearing two rings of slow digestion, and repeatedly removing one or the other ring to avoid its ``ring hunger'' effect, but always keeping at least one ring on to avoid normal food consumption. However, it is simpler to survive indefinitely by praying for food. When you pray successfully, your prayer timeout is set to rnz(350), assuming that you have neither been crowned nor killed the Wizard. rnz(i) can never be any more than 20 times i, so your prayer timeout cannot be any more than 7000.
If you pray successfully while starving, your nutrition level is set to 900. Assuming that you only consume one nutrition point every 20 turns (e.g., you are either a human wearing a ring of slow digestion or a xorn wearing an amulet of unchanging), it will take 18000 turns for your nutrition level to reach 0 (Fainting). This is more than enough time to ensure that you will be able to pray.
This strategy requires you to avoid being crowned, but as of version 3.4.1, you will never receive a favour for praying while in trouble and not on an altar, so this isn't a problem.
Here are some notes on how bones files work:
Is the number of bones files seen by a typical user in a typical game any greater on a multi-user system? The answer turns out to be: only if the users on the multi-user system are at differing levels of skill. If they are all at the same skill level and not improving over time, then the only relevant difference between the two systems is that more Nethack is being played on the multi-user system.
So what happens to the number of bones files on the system over time? Well, the number of bones files loaded (and hence removed from the system) in a typical game must increase with the number of bones files on the system. The probability of leaving a bones file in a typical game decreases if there are more bones files on the system - the average level reached before dying is the same (to a first approximation), but sometimes it won't be possible to leave bones because there is already a bones file for that level.
Therefore the more bones files there are on the system, the more are consumed and the fewer are created. Hence the number of bones files does not increase constantly over time, but reaches a steady state which is dependent on the average skill level but not the number of users. If the number of bones files on the system is the same on the single-user and multi-user machines, then the number of bones files seen during a typical game must also be the same.
On a system with varying skill levels, though, experts are likely to find more bones than they leave. Perhaps the easiest way to see this is to take an extreme case. If you are so expert that you ascend all the time, then on a single-user system you'll never leave or find bones. On a multi-user system, you'll still never leave bones, but there will be plenty there for you to find. If experts find more bones, newbies must find fewer (since the total number of bones files remains approximately stable).
Do bones files make the game easier or harder? On the one hand, you get to use or sell all the equipment in the bones pile (although it will mostly be cursed), but on the other hand, you have to watch out for whatever killed the former player. If the cause of death was a classic YASD like hitting a floating eye, then there's no problem. If it involved being ambushed by hordes of monsters, that is slightly tougher, but the hordes could have turned up on a new level at that depth too, and if the former player eliminated some of the hordes before dying, you are better off than if you were facing a brand-new pack. Problems arise when the original cause of death was something like ``gnome with a wand of death'' or ``wimpy hostile monster got lucky with a polymorph trap'' or ``player tried to genocide master liches with a cursed scroll'', or the former player had powerful pets.
Finally, on a multi-user system the bones files are going to be more varied and therefore more useful. If you stick to playing one class, there won't be much variety in the bones left on your own system, but on a multi-user system you'll find bones piles left by other classes with different equipment. Newbies on a multi-user system also have the chance of finding a bones pile left by an expert who suffered YASD with most of an ascension kit.