Similar to 'motorboating', a person rapidly jostles another's chest area with their face. However, in cases where breasts are too small, unsavory, or the target of the 'boating' is a male with defined pecs or gross 'moobs', this is met with the urge to throw up, cry, or play in traffic.
"I went to motorboat Joe's girlfriend but I ended up paddleboating her non-existant tits"
"I think Greg was drunk when he decided to paddleboat fat Steve"
"Chris's pecs were so hard I felt like I was paddleboating two boulders"