After a sluggish first month, the pace of coronavirus vaccinations is accelerating to the point that New York City and other places in the state expect to exhaust their supply of doses as early as next week, officials said on Friday, causing several health facilities to alter their immediate inoculation plans.On Thursday, Mount Sinai Hospital, one of Manhattan’s largest facilities, canceled many upcoming vaccination appointments for older patients, saying the doses it had anticipated receiving were no longer likely to arrive.