Here is a list of instruments that different Hetalia characters both can play and are thought to be able to play:

America- harmonica, acoustic guitar, bass guitar

Canada- violin, piano, banjo

2p!Canada- violin/fiddle

2p!America- guitar, electric guitar, dobro

Austria- piano

Prussia- electric guitar, drums

France- accordion

Iceland- violin

Germany- drums

Italy- guitar

Sweden- triangle

Norway- hardanger fiddle  

2p!England- violin, piano

Australia- didgeridoo, drums

Nyo!America- guitar, drums

Nyo!Canada- violin, flute, harp

Nyo!England- guitar, violin, piano

Nyo!Australia- drums, banjo

Nyo!Austria- piano

Nyo!Prussia- acoustic guitar, drums

Nyo!Italy- guitar

Nyo!Norway- violin/fiddle, hardanger fiddle

Nyo!2p!America- guitar, electric guitar, saxophone

Nyo!2p!Canada- violin/fiddle, piano, (wooden) flute

And here I will list any other characters (fanon/OCs/etc.) that I know of from various persons:

2p!Mexico- double bass, trumpet, tambourine
( my own OC )

2p!Māori- kōauau
( my own OC )

Ireland- violin/fiddle, banjo, harp, bagpipes, harmonica
( my own OC )

Northern Ireland- flute, harp, banjo
( my own OC )

Wales- violin/fiddle, piano, mandolin
( I have a lot of OCs... )

Scotland- bagpipes, harp

And now a list of characters that sing (some may or may not also play an instrument as well):

America
Canada
France
2p!America (occasionally)
2p!Canada (very rarely)
Egypt (occasionally)
Taiwan
Finland
Norway
Iceland (rarely)
Spain
Portugal (occasionally)
2p!Iceland
2p!Sweden
China
Romania
Ukraine
Hungary
Italy
Romano (very rarely)
2p!Romano
2p!England
Poland
Prussia
Belarus (very rarely)
Russia (rarely)
Liechtenstein
Hong Kong (rarely)
Australia
New Zealand (rarely)
Wy
Nyo!2p!England
Nyo!2p!America
Nyo!2p!China
Nyo!Australia
Nyo!Prussia
Nyo!Spain
Nyo!Portugal
Nyo!Norway
Nyo!Denmark
Nyo!Finland
Nyo!Greece (occasionally)
Nyo!Egypt (occasionally)

Aaaaaaand now a list of other characters (fanon/OCs/etc.) that sing (some may or may not also play an instrument as well):

Mexico
( fanon )

Māori
( my own OC )

Ireland
( my own OC )

Northern Ireland
( my own OC )

Scotland
( fanon )

Wales
( my own OC )

[if anyone has a character of any kind (canon, fanon, OC, etc.) they'd like to have added to theses lists just let me know and I'll add them on here ^ ^ ]