The frequency of radiation emitted by an oscillating electron is equal to its frequency of oscillation. For a simple L-C circuit (inductor and capacitor) that frequency is given by:

$\displaystyle f = \frac 1 {2 \pi \sqrt {LC}}$

where L is the value of the inductance in henries and C is associated capacitor in farads. See:

https://en.wikipedia.org/wiki/LC_circuit
The value of L for an air-core tightly wind coil with small gauge wire is:

$\displaystyle L = \frac 1 l \mu_0 N^2 A$

where $\displaystyle l $ is the length of the coil, $\displaystyle \mu_0$ is the permeability of free space, which is $\displaystyle \mu_0= 4 \pi \times 10^{-7} H/m$, N is the number of turns of the coil, and A is the cross-sectional area of the coil. Note that neither current nor speed of the electrons has anything to do with this. In fact, the speed of electron flow in a typical electronic circuit like this is really quite small: around 0.002 m/s. Hence radiation due to the electron's circular motion about the coil (known as Synchrotron Radiation) is negligible.