I use a 'drift' made from a length of 3/4" pipe with a hex brass cap (which is flat on top) on one end and an ordinary iron cap on the other. Parts are all available at Home Depot, just screw them together. To use it, set the brass against the bottom of the liner and smack the iron cap with a BFH. Move around the liner, just like driving out a bearing race.
In extreme cases, it may become necessary to break the liner into pieces. But I've only had to do that on engine blocks that have been left exposed to the elements for many years.
Bob's slide hammer does sound interesting, but I think that plate is going to have to be pretty carefully matched to the bore in the block and maybe the bore in the liner as well. Especially with 87mm (or worse yet 89mm) liners, the bottom edge is very thin. No problem at all if you have a lathe handy, but perhaps not so easy otherwise.