How can I sample a signal at 4 samples per cycle?
You need to understand that $f=f_s/4$ and "$4$ samples per cycle" are two ways of saying the same thing:

$$\text{ # samples per cycle}=\frac{f_s\text{ samples per second }}{f \text{ cycles per second}}$$

The number of cycles per second is equal to the ratio $f_s/f$, where $f_s$ is the sampling frequency, and $f$ is the signal's frequency.

So you just need a sampled sinusoid with a frequency $f=f_s/4$ (or, equivalently, $4$ samples per cycle). The value of $f_s$ is irrelevant.

$$x[n]=\sin(2\pi f\cdot n/f_s)=\sin(n\pi/2)$$

which is exactly what you have already come up with. Multiply this signal with your low pass impulse response, and you'll get a band pass filter centered at $f_s/4$.