During the second half of the 19th century and first half of the second, I have seen no mention of mercenaries fighting in the major conflicts of Europe. I'd love to know what happened to mercenaries (if anything) during this period of immense change in Europe.
While mercenaries were becoming a less prominent part of European conflicts they certainly still existed. For the Crimea War the British raised the Anglo-German Legion for example and the Franco-Prussian war was loaded with fighters for hire, quite a few American Civil War veterans for example. The Spanish Civil War was also full of foreign fighters from all over Europe fighting for ideology or pay. A fair few adventurous souls would also go off to serve as mercenaries in Africa or India.
That said, you're sort of right in implying that there was a definite lull in mercenary activity in this a rought 50-year period leading up to WW1. Quite a few factors could be used to explain this. There were no particularly interesting conflicts going on where either side was willing or able to pay for a significant contingent of foregin fighters. Towards the end of the period a lot of recruits were being drawn into their respective national armies.