Ttyjukl

In my Conworld's system, There is a small asteroid large enough to be a dwarf planet that has rings. How they got there, nobody knows. But could they have a prolonged orbit around the body without interference, unless from another asteroid?

Yup! This is possible, and a number of small bodies in the Solar System have rings:

• 
  Haumea, a dwarf planet in the outer Solar System, was recently discovered to have rings, which lie inside its Roche limit.


• 
  Chariklo, a very large asteroid, has two known rings.


• 
  Chiron, another minor planet, is suspected to have rings, but these have not been confirmed.

Minor planets orbit far away from each other and have such weak gravitational fields that they are unlikely to destabilize each other, barring an extreme close encounter.

These rings will eventually dissipate, as all rings do. Viscous spreading is one culprit, and for these minor planets, the effect may be more pronounced because of the nonexistence of shepherd moons around these bodies. In at least Haumea's case, an orbital resonance provides short-term stability, but not long-term stability.

10199 Chariklo

Picture Charlico

Nature bet you to the punch. This is 10199 Chariklo [1], a Centaur astroid orbiting between Saturn and Uranus. It has a radius of 151 km. As you asked for an elongated body, I see no reason why objects like these two couldnt have the same kind of ring system. In fact the artwork shown above could be inaccurate in showing an nearlt spherical body. Many astroids and comets we visited had weird shapes.

Eros pic

Ultima Thule pic

As for the zones where the rings could exist, the rings should be within the planets roche limit [2].

$r = 2.44 * sqrt[3]{frac{pp}{ps}}$

$r$ = roche limit

$pp$ = density primary object (your asteroid)

$ps$ = density secondary object (this was the object ripped appart to form the ring. Assume a sphere with the density of the rock-ice mixture you desire ($3 g/cm^2$ will work as an approximation))

This should give you the roach limit for a given object. Just place the rings somewhere inside it.

[1] https://solarsystem.nasa.gov/asteroids-comets-and-meteors/asteroids/10199-chariklo/in-depth/

[2] https://en.m.wikipedia.org/wiki/Roche_limit

Two implications.

1: A body large enough to be a dwarf planet that was cigar shaped.

http://www.astronomy.com/magazine/ask-astro/2017/08/the-diameter-of-spherical-bodies

For these igneous planetesimals, the diameter needed to overcome rigid
body forces and become round is about 620 miles (1,000km). The main
belt asteroid Vesta is 326 miles (525km) in diameter. In its early
history, Vesta’s interior was at least partially molten and may at one
time have been in hydrostatic equilibrium; however, after cooling,
Vesta was battered out of round by large impacts.

So something the right size that is not round has either been "battered out of round" like Vesta, or is of a composition such that it is much less dense than typical asteroids - maybe porous, like Hyperion. Or hollow...

2: An object with low mass might retain a ring thru electrostatics instead of (just) gravity. Electrostatics are relevant for existing planetary rings. Fast moving dust comprising the ring might be attracted by a combination of electrostatic attraction and gravity, and so persist around this lightweight cigar-shaped planetlet.