I revived this because I have a different way of playing it than the others above.
This is how the Maple Leaf Champions Jug Band do it. We do another verse too, but this'll give you the chords. I play the uke for this song and in the line that goes:
"If (C*) you (Em) like a (Am) ukelele (C) lady,
(C*) Ukelele (Em) lady like-a-(Am)you.(C)"
I use C*-5433, Em-0432, Am-2000, C-0003



UKELELE LADY
Gus Kahn & Richard A. Whiting

(C) I saw the splendor (G7) of the (C) moonlight
on Hono(Cdim)lu(G7)lu (C) Bay. (G7)
(C) There's something tender (G7) in the (C) moonlight
on Hono(Cdim)lu(G7)lu (C) Bay.
(Am) And all the beaches are full of peaches
(Em) who bring their ukes a(C)long.
And in the glimmer of the moonlight
they love to (D7) sing this (G7) song.

If (C) you (Em) like a (Am) ukelele (C) lady,
ukelele (Em) lady like-a-(Am)you.(C)
If (Dm) you (G7) want to (Dm) linger where it's (G7) shady,
(Dm) ukelele (G7) lady linger (C) too.(G7)
If (C) you (Em) kiss a (Am) ukelele (C) lady
and you promise (Em) ever to be (Am) true,(C)
and (Dm) she (G7) sees a(Dm)nother uke(G7)lele
(Dm)lady foolin' (G7) round with (C) you.(C7)

(F) Maybe she'll sigh, (an awful lot)
(C) Maybe she'll cry, (and maybe not)
(D7) Maybe she will find somebody else
(G7) By and by and by to
(C) Sing (Em) to (Am) when it's cool and (C) shady
When they're makin' (Em) wicky wacky (Am) woo,(C)
If (Dm) you (G7) like a (Dm) ukelele (G7) lady,
(Dm) Ukelele (G7) lady like-a-(C) you.