Designate one db the "owner" of the table, and force all inserts, updates and deletes to go there. Use a trigger and linked server to update the other tablein a synchronous fashion.

Or

Just have one copy of the table and use a synonym and a linked server, to make it look like two tables.

Or

inside the sp use service broker to send a message to the other server with the parameters, and execute the same logic there asynchronously.