If you are unable to find a paper with low enough contrast, another alternative is to shorten the exposure time by about 1/3, then flash the paper with a "not so safe light" I use a 7wt with an amber filter for approximately 10% of your exposure time. For example, you determine that 30 seconds should be abour 1/3 less than your "usual" exposure, so you would want to lightly flash the paper for 2.5-3.5 seconds. This lays down a gray mask overall similar to film.
Another alternative, would be run you piece of paper through developer before applying it to the pinhole camera. Be sure to squeegee or sponge drips off of it. Then expose first for approx. 1/2 of exposure time, then let the paper sit unmoved in the dark for about 2 minutes, then re-expose for 2/3 the normal exposure time, then re-develop as normal. Apparently the pre-exposure lays down and intelligent mask for the remainder of the exposure which effectively lowers contrast.
I tend to use multi-grade papers, which also give you the option of simply adding a low contrast filter over the pinhole.