It looks like another plot was initialized or clicked on after calling axesm, because this should work just fine:
figure
lonlim = [-60 120];
axesm('MapProjection','eqdcylin','Frame','on','Grid','on',...
'MapLatLimit',[-90 90],'MapLonLimit',lonlim, ...
'MeridianLabel','on','ParallelLabel','on','MLabelParallel','south')
coast = load('coast');
plotm(coast.lat,coast.long)
whereas this will produce the error message you're getting:
figure
lonlim = [-60 120];
axesm('MapProjection','eqdcylin','Frame','on','Grid','on',...
'MapLatLimit',[-90 90],'MapLonLimit',lonlim, ...
'MeridianLabel','on','ParallelLabel','on','MLabelParallel','south')
coast = load('coast');
figure % <-THIS WILL SCREW THINGS UP
plotm(coast.lat,coast.long)