You may be able to change the tuning of your kalimba. I had a commercially produced kalimba and the tangs were moveable by pushing/pulling them to become shorter/longer over the bridge which changes the tang's tuning. It's tricky to get the tuning right, but it's possible.

About your actual question: dealing with chromatic pitches on a purely diatonic instrument.

Think of this more as a strategy than a proper musical process. Sort of the way a jazz singer "interprets" a melody and changes pitches around. There isn't a "right" way to do it. Keep in mind chromatic tones are often the distinctive features of a melody, so changing those tones may sound like changes to the essence of the melody. Try to listen to substituted pitches with an open mind.

The first practical thing to do is to transpose all melodies you want to play into C major.

Next, the common reasons for chromatic tones are to form temporary leading tones, subdominants, or borrowed harmonies. Usually those temporary tones are relative to one of the diatonic tones. So, in C major...

• the temporary leading tones are C#, D#, F#, G# as leading tones those pitches would move up respectively to D, E, G, and A
• there is only one temporary subdominant Bb moving down to A (all the other temporary subdominants are diatonic and present no problem of chromaticism)
• the borrowed tones would be Eb, Ab, and Bb and they would likely be tones from borrowed chords, respectively the minor i, iv, or subtonic bVII

...that is just a list of the common harmonic origins of those chromatic tones. We want to know what to play as a diatonic alternative.

For the temporary leading tones you can alternatively play the whole step above the target note. Ex. for C# D try E D. The one place this will not work is D# E where the whole step above is another chromatic tone F#. In that case try playing B the dominant of E or just anticipate the E meaning play an E instead of D# before the main E.

For the temporary subdominant Bb try playing G to A, the whole step below the target tone.

All the above assumes the temporary leading tones/subdominant resolve by step to the next tone. If that doesn't happen in the melody, the most likely thing to happen in the melody will be those melody tones move to some other tone of the given chord. Conveniently all the other chord tones of the various chords involved will be diatonic tones. Ex. G# moving up to A, the G# is from the chord E7, the other tones of that chord are E B D, all diatonic in C major. Instead of playing the G#, try any of E B D.

For the borrowed tones try a similar approach of substituting with another tone from the borrowed chord. For example, if there is an Ab it is likely from a borrowed chord like minor iv, try one of the other tones from that chord like F or C. Conveniently, when dealing with borrowed tones Eb, Ab, and Bb and their respective chords i, iv, and bVII all the other chord tones are diatonic to C major.

It is very possible that a chromatic tone will be none of the chord tones above and will simply be a chromatic -non-chord tone_ such as a chromatic passing or neighbor tone. In such a case you have a bit more freedom to choose an alternative. Probably you can try whatever tone is diatonic in the other direction. Ex. for a lower chromatic neighbor, use the upper diatonic neighbor tone.

An example that I think works pretty well...

Red Roses for a Blue Lady

...with the chromatic tones changed according to my suggestions...