There is such thing as 'whistled' languages which rely solely on tone. Though they're all based on spoken languages. All the 'speaker' does is mimic the tonal pattern without pronouncing any phonemes. Such languages are used by hunters to communicate without alerting their quarry, because the language sounds just like bird song. But they don't use this language for most day-to-day communication.
As for a pikachu, well their 'words' are made up of three possible syllables: pi, ka, and chu. Thus a pikachu would have a total of 3 possible one-syllable words, 9 two-syllable words, and 27 three-syllable words. As we see, words would need to get quite long to get the possible vocabulary up to 100. Using tones though would easily multiply this. Even a simple two-tone system would double the number of possible syllables. Thus the syllable count would be 6 one-syllable words, 36 two-syllable words, and 216 three-syllable words. And there are real languages that have as many as 6 tones. With such a system, a pikachu would have 18 possible syllables to work with. Of course, you could say pokemon are more sensitive to tone than humans, which could increase the number of tones beyond what any human could manage.
Though a problem arises with cross-species communication. Obviously, no two species have the same set of syllables. Thus, for different species to be able to communicate with each other, the poke-language would probably have to be purely tonal, like a whistled language. Though you could 'multiply' the number of tones using length. A tone held for a short time could be considered a separate 'phoneme' from the same tone held longer. But we might just be fooling ourselves. The pokemon may just see a long tone as two identical tones right next to each other.
Most pokemon of course aren't intelligent enough to warrant a full-fledged language. Even Toki Pona would like contain some words they wouldn't make use of. Yeah, there's things like Alakazam which have an IQ higher than humans, but of course they can communicate telepathically, which would completely remove their need to use a language. And of course, there's some that can learn human language. Team Rocket's Meowth not only can speak, but he even taught himself how to! There's also one of the early movies which features a talking slowking. And one episode of the anime has a tenacool possessing meowth and speaking through him, which would imply it knows and understands human language, but lacks the ability to actually produce human sounds. Though honestly, its astounding that any pokemon could pronounce a human language. We have a lot of features in our mouths unique to our species that allow us to talk. Some birds in the real world can mimic human speech, but they accomplish this differently from how we do. I believe there is a pokemon in one of the later generations that can mimic human speech, though it can't understand language. By the way, the franchise is quite inconsistent as to whether pokemon can understand spoken speech or not.