I've shot a lot of handloads with .357 revolver bullets through my 336 over the years. Like the others, I haven't had much luck with bullets lighter than 150 gr. I get superb accuracy with Lyman # 358429 cast SWC bullets of 173 gr. in my alloy and the #358156 SWCGC at 158 gr. as well as several 158-180 gr. JHPs. Neither cast nor jacketed stuff under about 146 gr. seems to give groups anywhere near as consistent for me. I don't think it has much to do with twist rate, as the Marlin's is 1-16" just like most .357s. It may have as much to do with the Microgroove rifling and the velocities I've tried for as anything else.
My best groups with the cast bullets come in when I keep the velocity to about 1300 f/s or less. JHPs at about 1700. Neither hold up well accuracy-wise past 125 yds, as they don't have very favorable BCs and lose velocity quickly.