Some carriers in my country also limit the number of SMS a simcard sends per day.
On playSMS config file:
// limit the number of queue processed by sendsmsd in one time
$core_config['sendsmsd_queue'] = 1;
// limit the number of chunk per queue
$core_config['sendsmsd_chunk'] = 1;
// chunk size
$core_config['sendsms_chunk_size'] to 1 or 2, i.e. 1 or 2 sms sent each time.
above configuration will cause playSMS send one message a time.
What playsms version do you have?
On newer versions, playsmsd.conf has a parameter that sets sleep time between playsmd executions. Take a look.