A nine letter word for wooing might be romancing.
romancing
wooing
Flirting
I believe you would call them a Suitor.
The Wonderful Wooing was created in 1925.
The Minister's Wooing was created in 1859.
The Minister's Wooing has 578 pages.
Ye Wooing of Peggy was created in 1917.
The Reverent Wooing of Archibald was created in 1928.
Wooing Auntie - 1913 is rated/received certificates of: UK:U
The Warty Wooing - 1913 is rated/received certificates of: UK:U
The Scarlet Wooing - 1920 is rated/received certificates of: UK:A