You can set your own fee by using any script or API source you want (example).
The fee is merely “suggested” in Counterparty defaults, but you can change it (which doesn’t guarantee the transaction will be processed, it only makes the defaults lower). See the topic below.
If you don’t use the Counterparty client or API but you compose “raw” bitcoin transactions, you can send (broadcast) them directly from any Bitcoin full node and in that case it’s up to that node’s settings to accept the fee or not before it relays the transaction to the network.