Quickest way of multi-labelling images?
Your question is relatively devoid of details, so all I can really suggest is to use a standard convolutional network classifier.

The problem you seem to be having is that most such models output a one-hot vector, i.e., categorical distribution, corresponding to a single label: $p=(p_1,\ldots,p_n)$, where $\sum_i p_i = 1$ and $p_i$ is the probability of assigning label $i$ (and only label $i$) to the input. Usually this is computed via $p = \text{SoftMax}(f_\theta(x))$ for some input image $x$ and neural network $f_\theta$.

To change this to handle multiple labels, let $q=(q_1,\ldots,q_m)$, where $q_i\in[0,1]$ is the probability of assigning label $i$ to the input. You can think of each $q_\ell$ as parameterizing a Bernoulli distribution over a single label. You can compute $q$ via, for instance, $q = \sigma_E(f_\theta(x))$, where $\sigma_E$ is the elementwise sigmoid function. You can then assign labels to $x$ by, for example, thresholding each $q_j$, i.e., assign label $k$ to $x$ if $x_k \geq T$, where $T$ is a hyper-parameter that can be, say, 0.5.

In other words, take the classifiers on Github and replace the softmax with an elementwise sigmoid, change $n$ to $m$, and use your training data; that's it. 

Hopefully that's what you meant.