I asked CPS about rechargeable batters just last week. As long as the batteries do not contain Lithium and the total number of non-lithium batteries being shipped doesn't exceed the number/weight (which is a lot) that would qualify the shipment as being dangerous goods, no problem with CPS.
Lithium batteries are the issue and it is the airlines that are ultimately restricting them being loaded onto their planes, not necessarily the courier companies. There are provisions where you can ship lithium batteries but these batteries must meet several conditions that would allow the battery(s) to be accepted for transportation on an aircraft. The onus is on the shipper to provide a declarations stating that their lithium battery shipment complies with the requirements. It is my experience that a courier company seeing or reading any mention of a lithium battery being included in the shipment begins a process that usually results in that item being held and classified as dangerous goods. Surprisingly cellphones which all contain a lithium battery seem to sail straight through Miami without issue.
This is pretty much a lack of training when it comes to batteries and a general belief that all lithium batteries are restricted which is not the case. When dealing with Dominican courier companies it is usually an uphill fight to have them deliver lithium batteries to you here in the DR.
The webpage below will give you the ammunition to explain why your lithium battery is perfectly fine to transport to the DR on an aircraft but your success rate in actually convincing the company to put the lithium battery on said aircraft may vary.
See page II Section II - "Acceptable to all locations"
http://images.fedex.com/downloads/shared/packagingtips/lithiumbatteryFlowChart.pdf