I would use an engineer. While these are not traditionally "devices", left to "his own devices" a bored engineer will measure most things

You would use outside calipers for the external diameter and inside calipers for an internal diameter:

You could use just about anything that measures a straight line, since a diameter is a line - like a ruler, or calipers, yardstick, etc.

Ah wait a sec - perhaps you meant a SPHERICAL object. Then the calipers would do the best job. The ruler wouldn't be much good. :o) And a tape measure would give you the circumference, not the diameter.

A calliper.

1) Inside diameter or outside diameter?
How big is the object diameter approximately, in a scale from an atom to a galaxy? (e.g. the Moon)
What is the form of the object exactly? Spherical? Cylindrical? With fixed or variable diameter?
Is it possible to touch the object with anything or will it explode or disappear (e.g. soap bubbles)?
Is the object moving? How far is it?
Is the whole diameter part of the object? (e.g. spherical diameter of a lens, half a ball?
Maybe the angular diameter?
http://en.wikipedia.org/wiki/Angular_diameter


2) You could also calculate it. Like for instance, "Eratosthenes, who calculated the diameter of the Earth around 240 BC."
http://en.wikipedia.org/wiki/Diameter

"Calculate the diameter of hair by measuring the diffraction fringes."
http://physicslearning.colorado.edu/pira/PiraSubTOC.asp


3) a ruler:
http://media.nasaexplores.com/lessons/01-032/k-4_1.pdf


4) a caliper. Here again, ther are many types:
"1 Types
1.1 Inside caliper
1.2 Outside caliper
1.3 Divider caliper
1.4 Oddleg caliper
1.5 Vernier caliper
1.6 Dial caliper
1.7 Digital caliper
1.8 Micrometer caliper "

"A caliper (British spelling also calliper) is a device used to measure the distance between two symmetrically opposing sides. A caliper can be as simple as a compass with inward or outward-facing points. The tips of the caliper are adjusted to fit across the points to be measured, the caliper is then removed and the distance read by measuring between the tips with a measuring tool, such as a ruler.

They are used in many fields such as metalworking, mechanical engineering, gunsmithing, handloading, woodworking and woodturning."
Source and further information:
http://en.wikipedia.org/wiki/Caliper

Further information:
http://en.wikipedia.org/wiki/Cruising_rod


5) a micrometer:
"A micrometer (pronounced /mаɪˈkrɒmɪtər/) (enPR: mī-krŏmʹĭ-tər), sometimes known as a micrometer screw gauge, is a device used widely in mechanical engineering and machining for precisely measuring, along with other metrological instruments such as dial calipers and vernier calipers. Micrometers are often, but not always, in the form of calipers.

Colloquially the word micrometer is often shortened to mic"

"- Basic types
The image shows three common types of micrometers; the names are based on their application:

Outside micrometer (aka micrometer caliper)
Inside micrometer
Depth micrometer
Bore micrometer
Tube micrometer
An outside micrometer is typically used to measure wires, spheres, shafts and blocks. An inside micrometer is commonly used to measure the diameter of holes, and a depth micrometer typically measures depths of slots and steps. The bore micrometer is typically a three anvil head on a micrometer base used to accurately measure inside diameters. Tube micrometers are used to measure the thickness of tubes.

- Specialized types
Each type of micrometer caliper can be fitted with specialized anvils and spindle tips for particular measuring tasks. For example, the anvil may be shaped in the form of a segment of screw thread; in the form of a v-block; in the form of a large disc; etc.

Universal micrometer sets come with interchangeable anvils: flat, spherical, spline, disk, blade, point, knife-edge, etc. The term universal micrometer may also refer to a type of micrometer whose frame has modular components, allowing one micrometer to function as outside mic, depth mic, step mic, etc.

Blade mics have a matching set of narrow tips (blades). They allow, for example, the measuring of a narrow o-ring groove.

Pitch-diameter mics have a matching set of thread-shaped tips for measuring the pitch diameter of screw threads.

Limit mics have two anvils and two spindles, and are used like a snap gauge. The part being checked must pass through the first gap and must stop at the second gap in order to be within specification.

Micrometer stops are essentially inside mics that are mounted on the table of a manual milling machine or other machine tool, in place of simple stops. They help the operator to position the table precisely."
Source and further information:
http://en.wikipedia.org/wiki/Micrometer_%28device%29


6) Diameter Tapes:
http://www.newmantools.com/gauge/dtproducts.htm

http://www.raft.net/.../...suring%20Tape.pdf


7) "Star gauge (Ordnance), an instrument for measuring the diameter of the bore of a cannon at any point of its length."

"Wire gauge, a gauge for determining the diameter of wire or the thickness of sheet metal; also, a standard of size."
Source:
http://dictionary.die.net/rain%20gauge


8) Conflicting measurements:
"How big is 2003 UB313 -- the most distant known object in our solar system -- often referred to as the "10th planet"? Ever since its discovery, the exact size of this object, nicknamed "Xena" by its discoverers, has exercised planetary scientists. In the past week, two different announcements gave conflicting answers to this question. One put 2003 UB313's diameter first at almost precisely that of Pluto, the other at 30% greater than Pluto. "
Source and further information:
http://www.planetary.org/.../...cent_Studies.html


9) further inventions:
http://www.freepatentsonline.com/5103571.html
http://www.patentstorm.us/patents/6543151-description.html

the circumference is pi x the diameter

a measuring tape, a calculator and Pi

a micrometer

you would use a micrometer

A piece...of... string