I think you need something starting with B, just because you'd then have J B J B which is SO cool.... my family is J C J C which is awesome!

Brielle (probably too close to Brianna though)
Brodie
Brady
Bethany
Bethan (Welsh, unusual but nice)
Bonnie
Blythe
Brennan (again probably too close to Brianna but I love it)
Brandi
Briar
Brittany/Britney/Britt
Bryn
Bronya
Brooke
Bronwyn/Bronwen

Hope this helps!