Judy of POSSIBILITIES, etc.! and FREEBIES, etc.! has posted a tutorial for stitching a basketweave border around any odd shape. She says,
Having seen a number of people having trouble stitching basketweave around shaped ornaments, I have begun a tutorial … to show step by step how really simple it is. By doing basketweave, the ornament canvas won’t warp, and as always, is much smoother and prettier – it becomes second nature when you understand the correct method of stitching.