We're putting our kid (due in 6 weeks) in a hammock craddle next to our bed and I want to work out a way how to gentle rock it.

The craddle looks like this:



And I want the craddle to rock back and forward like so:



There has to be a way that I can attach something (spring loaded...?) to the carabiner to make it move back and forward but I can't work out what. Any ideas?