I already have used ~,<,>,’,=,-,^, and v for trills, rising tones, falling tones, glottal stops, chord tones, neutral tones, rising/falling tone, and falling/rising tone. This language is structured like music. Letters in exponents denote the lowest part on a chord, or the final tone in any other sequence. All moving tones are 3 tones except trills, which are 4 tones. Are there any other keys on a standard english keyboard that could be used and make sense for whistling? Please include how to get the character if option is used.
If one of your main goals is to be easy to type, I'd recommend repurposing Latin letters. This is quite common in real-world languages, since a lot of international standards are now based on the English alphabet.
The Romanized Popular Alphabet, for example, repurposes miscellaneous letters for the tones of Hmong (aka Hmoob). B indicates a high tone, s a low tone, j a falling tone, v a rising tone, m or d a creaky tone, and g a breathy tone. There's no inherent connection between these letters and the tones they represent, but they're easy to type and won't cause issues on passports and official documents.
If you don't want to use letters, it would help if you explained your goals in more detail (like what other things you're trying to represent).