Depending on which marketplace you're talking about, but I know that Amazon doesn't want you to solicit any of their buyers since they already do it for you. On eBay, you can usually ask for feedback.

A tactic I've used is to include a reminder note within the package or packing slip that reminds the buyer how important feedback is for you and the marketplace.

I don't recommending using any software to request feedback because it's looked down upon by marketplaces is general.

Hope this helps