You can define one coulomb as one ampere-second but that is of little value in giving students a picture of it. Talk of coulombs as things that go round the circuit, the things that you might count flowing past any point you might choose in the circuit, much as a policeman might count ‘cars per minute’ for traffic flow or a hydraulic engineer ‘gallons of water every minute’. In electric circuits scientists and engineers count coulombs per second and call them amps.
Introductory level ideas
At introductory level, students need only have the idea that 'something' flows around a complete circuit, transferring energy from the power supply to devices such as lamps.
Worries about absolute standards and units belong in advanced level teaching and not in an introductory scheme of activities. Students accept the kilogram as a well understood unit when it is no more than a copy of some chosen standard.
If students ask how anyone knows the size of a coulomb, the best reply at introductory level is that you simply read the ammeter which tells the rate at which coulombs are passing and multiply by the time in seconds. That puts the blame for the definition on the ampere, and the ampere you could say is defined by the reading of a standard ammeter kept at some standardizing laboratory in each country in the world. You may need to point out to students how one ammeter can be compared with another and that in turn with a standard ammeter.
Intermediate level ideas
At intermediate level, instead of saying what things are travelling in a circuit, electrons or electric charges, emphasize a cruder view. Say that something travels that you measure in chunks called coulombs. Coulombs travel along a wire in a circuit and you can count them as they go by with an ammeter and a clock.
Students need to be equally confident in expressing some energy transfers in joules per coulomb. You can price oranges in pence per dozen, or milk in pence per litre, knowing quite well what kind of things a dozen and litre are. So, make a coulomb too almost real, by tracing it round the circuit pushed by coulombs behind it and pushing the coulomb in front (by means of electrostatic fields), slipping smoothly through low resistance, banging its way through high resistance, shoving against the edges of the armature-wires in a motor, carrying the material of chemical ions across with it in electrolysis; always paying out joules as it goes.
Say a current of 2 amps means that 2 coulombs of electric charge pass each point in a circuit every second. Then whenever you give pupils data, ask them to interpret it: the current is 2 amps; that means 2 coulombs per second. If the current is 5 amps, how much charge passes a given point in 10 minutes?
Advanced level ideas
In advanced courses, 1 amp is defined as the current which when flowing in each of two infinitely long parallel wires one metre apart produces a force of 2 x 10-7 newtons on each metre of either wire. That definition has two virtues: it reduces the number of arbitrary standard units and it makes it possible to carry out some very important calculations; e.g. the force on a current-carrying coil placed in a region near another current-carrying coil. This should not worry beginners to the subject.
Students may ask if a coulomb is the same kind of thing as an electron. Say that you can think of the electron as a very tiny particle which has a mass like any other piece of matter but also carries a charge. A coulomb is the charge of a vast number of electrons. In fact the size of an electron’s charge can be measured in coulombs; that means experimentally comparing two sizes, one electron charge and one coulomb of charge, i.e. Millikan’s experiment.
One electron charge = 1.6 x 10-19 coulomb
One coulomb is 6 x 1018 electron charges
A coulomb is always 6 x 1018 electron charges but in many cases of currents (e.g. in conducting solutions, in gases and in some semiconductors) some of those charges are negative and moving one way and the rest are effectively positive and are moving the opposite way.
If we were beginning the development of the science of electricity all over again in the twenty-first century, we might well take the electron charge as our basic unit instead of the coulomb. But electricity is too well established for us to make that change comfortably. Also the electron charge would prove far too small for convenient use in many practical applications.