Your problem was already considered by the SE Community: Relay contact sticking while driving a capacitive load
This TE relay is a good device (already used, but I prefer Omron or Finder because they characterize their relays better), and as Tony Stewart said can be used reliably up to 1 A at your 48 V. Between us, if you relax the expected life in terms of number of operations (e.g. you operate the relay rarely), then you can increase a bit the operating current.
As you say, the inrush drained by the capacitive load could stick your contacts for excessive heat. What matters is the dissipation in the relay contacts, for which we do not have the contact resistance value.
Usual solution is a series NTC or -- better -- a series inductor. We don't know the time of closure of the electric contact (not the mechanical operation), but we can assume something in the order of 10-100 us; if shorter the inductor will have a larger reactance, solving the problem completely. At 100 us the 22 uF has values of reactance XC in the order of few ohm: the inductor must provide enough reactance XL to limit the current. Let's say that XL is slightly larger than XC; then you end up with about L=100 uH. At 10 us XC will almost disappear increasing the theoretical inrush current value, but XL will be ten times larger.
[Update after comment on possible resonances] If an inductor is not a viable solution, then the NTC is, at the cost of some dissipation. For bulky slower inrush an auxiliary relay can be used to short circuit the dampening resistor, so putting together a "mechanical NTC".
-- Otherwise a solid-state relay may be used. -- I prefer mechanical relays with double contacts (so 2-wy relays) and I put the contacts in parallel: in case of asymmetry (or pristine wearing of one contact), the one heating up sees its current going into the other and this ensures some protection.