Deploy two independently hosted services in production at once without any downtime
I think you're taking the problem on the wrong side, you may start a whole new infrastructure aside and then switch loadbalancers from blue to green, loosing sessions, breaking ongoing transactions etc.

The proper way to achieve what you're doing is coding differently, when A relasease a breaking API ni version n, a should be able to continue to answer call to api in version n-1. the usual method is to have the version in the uri or an header, for exemple:

&lt;a-host&gt;/api/1/getCustomers and &lt;a-host&gt;/api/2/getCustomerList (for exemple if n is 2). With that, you can do a rolling update of B, with backends still using api v1 and new ones using api v2.