In this particular case, inverting the CDF is probably easier. But if you want to use rejection sampling then trying sketching the PDF. It is convex downwards, so a straight line that touches the PDF at the two interval endpoints will be above the PDF everywhere in between. That gives an ok rejection sampling scheme.

You could also make an adaptive rejection scheme: sample a point $x_1$, which involves computing $f(x_1)$. You can now use a pmf that's a straight line on $[1,x_1]$ and a straight line on $[x_1,2]$ for rejection. When you sample $x_2$, use it to split one of those intervals. After you sample $k$ points you will have a proposal density made of $k+1$ lines, which will be very close to the true pmf.

In this case that's not worth the effort, but a somewhat similar form of adaptive rejection sampling on the log pmf was used in the BUGS MCMC system (I don't know if it's in use for JAGS)