I have a Toro recycler lawnmower with the Briggs & Stratton seven horse 190 CC L-head engine with electric start. The problem is when I go to start the mower and use the electric starter, even with a fully charged battery , it will crank over for a minute or two before it’ll finally starts, usually puffing a little black smoke. When I’m trying to start it with the electric starter and stop and use the pull starter, it will usually fire right off in one or two pulls. Could this be a coil problem or carburetor? It will fire up a little better using the electric starter when it’s hot, but not much. It started doing this about a year or so ago. Would like some advice before I start throwing parts at it. Other than that, the engine runs great and after 11 years doesn’t use a drop of oil. Thanks in advance.
Ted

From what you post, can we say that the engine is cranking over a bit quicker by hand?
 
It sounds like it's, on battery, isn't spinning fast enough.  It's getting fuel (from the 
black smoke upon start up) so fuel isn't the issue.
 
You didn't mention anything about being hard to pull so I'd suspect the 
compression release is fine..
 
That would leave me looking at the battery-Get it load tested.
Check tightness of all battery to starter cables. 
 
Lastly, the starter may be worn out, cranking over slow..
 
.