Good suggestion Alex but this company is owned entirely by the Scottish Government, so there is no chance of them giving over taxpayers money as sponsors.
The company is owned by the Scottish Parliament but is run as a Private Ltd Company and I believe the taxpayers money that went into saving the company and the airports has been recovered long since. This company operates in the black and is making decent profits. Bearing in mind that advertising generates income I dont think the parliament would object to some of the profits being used for such purposes. Besides advertising budgets are tax deductable so it would mean a little less going to the UK treasury.
From hial.co.uk:
Highland and Islands Airports Limited (HIAL) is a public corporation wholly owned by the Scottish Ministers. The company operates and manages 11 Airports at Barra, Benbecula, Campbeltown, Dundee, Islay, Inverness, Kirkwall, Stornoway, Sumburgh, Tiree and Wick. HIAL's airports are vital to the social and economic welfare of the areas they serve, but are loss making, and are supported by subsidies from the Scottish Government in accordance with Section 34 of the Civil Aviation Act 1982.