If you go by train, you'd have to change in Zagreb. Never done it, but it should be interesting. Maybe redpaddy or t_maia can help, they're more experienced in travelling in eastern Europe than me. München-Zagreb is approx €90 for a standard ticket, but it should be possible to get it cheaper than that. Zagreb-Split shouldn't be expensive.
Given the fact that Zagreb is a major detour, you might be quicker if you went by bus through Italy. Rumour on the web has it there is a direct bus from München to Split that leaves on thursdays, but I haven't been able to find out with which company. Best go down to the central bus terminal, just off Central station.
update
Eurolines has a direct bus daily from München to Split. Tickets start at €63 for a single trip, €98 for a return.
[ Edit: Edited on 28-May-2009, at 06:25 by bentivogli ]