How can I manipulate the time signal to insert zeros in between frequency domain bins?
Assuming the OP wants to manipulate a time domain function such that zeros are inserted in the frequency domain result, here is a simple approach:

Simply replicate the time domain samples and then divide by the number of repetitions to normalize and this will result in the same frequency domain result as the series that was replicated, with additional zeros inserted based on how many times the time domain sample was replicated. 

Here is a simple example:

$fft([1, 2, 4, 2]) = [9,  -3,  1, 3]$ 

To insert one zero in between each sample repeat the time domain sample once and divide by 2:

$fft([1,2,4,2,1,2,4,2])/2 = [9, 0, -3,0, 1 ,0, 3]$ 

To insert two zeros in between each sample repeat the time domain sample twice and divide by 3:

$fft([1,2,4,2,1,2,4,2,1,2,4,2])/3 = [9, 0,0, -3,0,0, 1 ,0,0,3]$ 

It might be easier to understand how this occurs when you insert zeros in the time domain which causes repetition of the signal in the frequency domain over the duration of the DFT signal. This is explained in further detail here with regards to interpolation using zero-insert:

Upsampling and comb function